Free Homework Help
http://schooltutoring.com/help
Our education staff publish regular articles, tips and tutorials to help students with their homeworkThu, 23 Mar 2017 04:09:20 +0000en-UShourly1https://wordpress.org/?v=4.6.475589453Math Review of Problem Solving with Systems of Equations
http://schooltutoring.com/help/math-review-of-problem-solving-with-systems-of-equations/
Thu, 23 Mar 2017 04:09:20 +0000http://schooltutoring.com/help/?p=9114Overview
Systems of two equations with two variables can also be used to solve problems. In order to solve the problem, it can be translated to a system of equations. Once the problem is understood, students can make a plan, find the answer, and check to make sure it is correct.

Understand the Problem

In order to understand the word problem, read it very carefully and note the questions asked, the data given. Pay attention to any word cues that indicate mathematical relationships. Suppose a basketball team played 180 games and they won 40 more games than they lost. How many games did the team lose? In that case, the team played 180 games total. 40 more games were won than lost.

Make a Plan

In making a plan, write a system of equations to fit the problem. Let x be the number of games won and y be the number of games lost. In the first equation, x +y = 180. In the second equation, x –y =40. Those equations can be combined to find the answer.

Find the Answer

This system of equations can be solved by the addition method, as x +y = 180 and x-y = 40. Therefore 2x +(y-y) = 180 +40, or 2x= 220. Solving for x, divide both sides by 2, so x =110. Solving for y, 180 -110 = 70.

Check the Work

To see if both sentences are true, 110 +70 equals 180, and 110-70 equals 40. The same sort of process can be used to solve equations by choosing the substitution method. Suppose that Matilde is 13 years older than Ana. In 9 years, Matilde will be twice as old as Ana. Let x be Matilde’s age and y be Ana’s age. There are two equations in the plan, x =y +13, and x +9 =2(y +9). Using substitution, x = y + 13, and x = 2y +9, so y +13 =2y +9, so y = 13-9, or 4. Ana is 4, and Matilde is 17. In 9 years Matilde will be 26, and Ana will be 4+9 or 13. Matilde is twice Ana’s age in 9 years, and the answers check.
Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Farmville, VA: visit: Tutoring in Farmville, VA]]>9114English Review of Paragraphs
http://schooltutoring.com/help/english-review-of-paragraphs/
Wed, 08 Mar 2017 04:07:10 +0000http://schooltutoring.com/help/?p=9108Overview
Individual sentences express complete thoughts, and individual paragraphs support main ideas. The development of paragraphs flows naturally to the development of arguments to support a central idea.

Paragraph Length

All the sentences in a paragraph support one main idea. Suppose a journalist were writing an article about a city meeting. She may choose to start the article “The City Council held a meeting at City Hall on February 2 at 7 PM to take recommendations for the location of the new building for the Boys and Girls Club.” The chairman of the local Boys and Girls Club would like it in the same area in Smallville, while the owner of property in Gotham City wants the new building built on their land. However, a student writing an essay for their government class might use the same meeting information, but slant it in a different way. “The City Council holds regular meetings every two weeks to ensure public input on issues important to the community. Last month, they held public meetings to discuss funding for the new library. The most recent meeting was to discuss the location of the new Boys and Girls Club building. The proposed agenda for their next meeting will continue discussion of its funding.”

Relating Main Ideas to Central Themes

The central theme of an article or a nonfiction essay is often called a “thesis statement.” The newspaper article has the central theme recommendations for possible locations. For example, the chairman of the Smallville Boys and Girls Club wants it in the existing location. The property owner in Gotham City wants it built on their property. Another sentence might discuss the proposal by the chairperson of the Chamber of Commerce to build the Boys and Girls Club near the ball fields at the edge of town. In contrast, the government paper has the central theme of different types of City Council meetings in the community. The City Council held one meeting to discuss public input into library funding, one to discuss the location of the Boys and Girls Club building, and one to discuss how the new building will be funded. The main idea of each paragraph will relate back to that central theme or argument.

Narration in Paragraphs

Paragraphs can be organized as narration or description. The first paragraph of the newspaper article is an example of narration. The first sentence tells who had the meeting (the City Council and the public), where and when the meeting took place (City Hall, February 2, at 7 PM), what (the meeting), as well as why (proposals for the location of the new building). The chairperson of the Smallville Boys and Girls Club spoke first, then the landowner, then the chairperson of the Chamber of Commerce, and so on. A descriptive paragraph might tell the reasons why the chairperson of the Boys and Girls Club wants the new building at the existing location. The existing location is in a safe place, with plenty of outdoor lighting. It is easy to get to by biking, walking, or riding the bus. It is close to the middle school, but it is away from places where people live, so kids can make noise without a lot of complaints from neighbors.

Process in Paragraphs

Some paragraphs describe a step-by-step process. For example, when a building is built, first a plan is made, then the location is excavated, then the foundation is poured, and so forth. Other types of paragraphs describe classifications. One sentence can describe public meetings, another, the city newsletter, another, televised reports from each city department, and still another, legal notices in the daily paper.
Interested in English tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Middlebury, VT visit: Tutoring in Middlebury, VT]]>9108English Review of Sentences
http://schooltutoring.com/help/english-review-of-sentences/
Sun, 26 Feb 2017 20:56:20 +0000http://schooltutoring.com/help/?p=9103Overview
A sentence is a group of words that form a complete thought. There are different types of sentences depending on what they contain.

Complete Sentence

Students are often asked to write answers to essay questions in complete sentences. A complete sentence has a noun that acts as a subject, and a verb that is either an action or a state of being. Suppose students are reading a book chapter in chemistry about the periodic table. They are asked to use complete sentences to describe it. One student might write “The periodic table contains metals, nonmetals, and transition elements.” Notice that the sentence has a subject and a verb.

Phrases and Clauses

Phrases cannot stand alone, because they do not contain a complete thought. If the phrase is the yellow cat, what is it doing? Is it sitting on the step, or is it chasing a squirrel? Similarly, suppose the phrase is “flying an airplane.” Who is flying the airplane and where is it going? The answer might be different if the pilot is flying the airplane along the Polar Route, or the hijacker is flying the airplane into the desert. If the sentence isn’t complete, there’s not enough information.

Kinds of Sentences

Sentences are classified based on the amount of information they contain. A simple sentence has only a noun and a verb, with one clause. “The cat ran across the backyard.” The phrase “across the backyard” describes one thing, where the cat ran. A compound sentence has two or more separate clauses, such as “The cat ran across the backyard, and the dog barked. “ Those clauses are joined by a conjunction, such as or, and, or but. A complex sentence has one relative clause, such as “The cat, which was carrying a squirrel in its mouth, ran across the backyard.” A complex-compound sentence has at least one relative clause, as well as two separate clauses. “The dog, which was lying in the sun while gnawing a bone, barked; and the cat streaked across the backyard, when the car revved its engine.”

Purposes of Sentences

Declarative sentences tell a complete thought. The dog barked. The sun rose. The bell tolled. They end with a period, and are the most common types of sentences. Interrogative sentences ask questions, and end with question marks. Why is the sky blue? What is the weather like? Where are you going? Exclamatory sentences show excitement, and end with exclamation points. That was the best movie of the year! I hate weeds! Spring is coming! Imperative sentences are commands, and usually omit the subject “you.” Make it so. Drive on.
Interested in English tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Ogden, UT visit: Tutoring in Ogden, UT]]>9103Science Review of Storms on the Sun
http://schooltutoring.com/help/science-review-of-storms-on-the-sun/
Sun, 12 Feb 2017 23:52:15 +0000http://schooltutoring.com/help/?p=9096Overview
Eruptions of light and other forms of radiation from the sun affect conditions on and near Planet Earth, causing geomagnetic storms, solar radiation storms, and radio blackouts. Some types of “storms on the sun” include solar flares, coronal mass ejections, high-speed solar wind, and solar energetic particles.

Solar Flare

Solar flares come from the release of magnetic energy associated with sunspots. We observe them as bright areas on the sun that can last anywhere from minutes to hours. A solar flare releases energy from visible light throughout the spectrum, including x-rays and ultraviolet light. They impact Earth when they occur on the side of the sun that faces us, because the energy-carrying photons travel in straight lines.

Coronal Mass Ejections

The outermost atmosphere of the sun is called the corona, shaped by strong magnetic fields. If the fields are closed rather than open, parts of the confined solar atmosphere can suddenly erupt, releasing bubbles of gas and solar material in a violent explosion. Tons of matter violently burst through space at millions of miles an hour, impacting anything in its path. The cloud has to be facing Earth to affect the planet.

High-Speed Solar Wind

The solar wind is formed along magnetic fields that travel through the Solar system, from large, dark areas in the sun’s corona called “coronal holes.” Open lines in the sun’s magnetic field allow particles to be more accelerated, creating a high-speed solar wind. If the high-speed solar wind is formed near the equator of the sun, it is more likely to create shock waves that release more energetic particles.

Effects on the Earth

If the magnetosphere of the Earth is impacted by energy from any type of storm on the sun, it undergoes sudden and repeated change. For the most part, the magnetosphere protects us from most particles the sun emits. However, if that stream of magnetic particles is unusually strong or hits the magnetosphere southward, it can enter the atmosphere at the poles and weaken the magnetic field of the Earth (or any other planet it encounters). Although the magnetic field goes back to its normal strength in a number of hours, during the time the magnetic field is interrupted, electrical and radio communications can be brought down. For example, the electrical blackout that affected 6 million people in 1989 was caused by a geomagnetic storm, and radio disruptions often affect aircraft communications.
Interested in science tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Austin, TX visit: Tutoring in Austin, TX]]>9096Science Review of the Eight Senses
http://schooltutoring.com/help/science-review-of-the-eight-senses/
Sun, 29 Jan 2017 04:25:28 +0000http://schooltutoring.com/help/?p=9091Overview
The five senses of vision, hearing, touch, taste, and smell are familiar. However, people have three more senses that are critical to everyday life –vestibular, or sense of balance; proprioceptive, or sense of where one is in space; and interoceptive, or the body’s sense of what is going on internally. Although those senses are not as familiar, they are necessary to optimal functioning.

Vision and Hearing

The visual system includes the eyes and the occipital lobe of the brain. The eyes process stimuli from light in a complex relationship between special cells and nerves. Connections between the eyes and the brain allow people and animals to make sense of the landscape, to recognize what is being seen, and to detect features and movement. The auditory or hearing system includes the ears and parts of the brain that are critical to hearing, such as the primary auditory cortex in the temporal lobe of the brain. Just as light can be perceived in hue, brightness, and saturation, sound can be perceived as pitch, loudness, and timbre (the type of the sound).

Taste, Smell, and Touch

There are only four qualities of taste; bitter, sour, salty, and sweet. Taste buds in the tongue are most sensitive to those separate qualities, which depend on chemicals in the food substances. People and animals learn to distinguish between them. Areas of the brain responsible for processing taste information include specific parts of the medulla. Smell is also a chemical sense, and the primary organ of smell is within the nose. Specific areas within the brain include the amygdala, neocortex, and hippocampus in the base of the brain. Taste and smell are closely related, which is why food tastes so bland when the nose is stopped up with a cold. Touch, in contrast, involves the body’s largest organ, the skin. Elements of touch include touch, pressure, temperature, and pain. The brain and spinal cord process tactile, or touch, information from many different places, including the parietal lobe, the thalamus, and multiple locations along the spinal cord and cranial nerves.

Vestibular

The vestibular system includes systems that control balance, keeping the head upright, and adjustment of eye movement to compensate for head movements. (Think of the eye movements of a dancer pirouetting across the stage. She keeps her eyes focused on the same point to prevent becoming dizzy as she turns.) It consists of the semicircular canals and the vestibular sacs. Those systems connect with specific cranial nerves and parts of the brain, such as the cerebellum, medulla, and spinal cord.

Proprioceptive and Interoceptive

The proprioceptive sense is the way the body senses the position, location, orientation, and movement of muscles and joints. Sensory information comes from connections between the inner ear with special receptors in every muscle and joint in the body. That sensory input travels to areas in both the cerebrum and cerebellum. Interoceptive senses involve the way that processes are coordinated within the body, such as hunger, thirst, and many other feelings necessary to life. Scientists have identified many other senses which are not as well-known as these eight, and some have suggested that people may have as many as 39 separate senses.
Interested in science tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Mount Juliet, TN visit: Tutoring in Mount Juliet, TN]]>9091Math Review of Solving Systems by Addition
http://schooltutoring.com/help/math-review-of-solving-systems-by-addition/
Sun, 22 Jan 2017 20:39:51 +0000http://schooltutoring.com/help/?p=9083Overview
Besides solving systems of equations by graphing and substitution, systems of equations can also be solved by addition. Math students can choose the best method for the problem at hand. Sometimes this process is called “solving systems of equations by elimination”.

Using Addition

Although some systems of equations can be solved by substitution, other systems can be solved by adding both equations. Both equations must be written in standard form as Ax +By =C. For example, suppose the equations in the system are x +y = 5 and 2x –y = 4. They can be expressed as x +2x +y –y = 5 +4. Now x +2x equals 3x, y-y = 0, and 5 +4 = 9. The new equation is 3x +0 = 9, or x =3. If 3 +y = 5, then y equals 2. Checking the solution in the second equation, 2x or 6 -2 does equal 4. The addition method can be used because the addition property for equations states that we can add the same number to both sides of the equation, and the equations are still equivalent expressions, and make a true statement.

Using Multiplication, Then Addition

The multiplication property of equations is an extension of the addition property, since multiplication is repeated addition. Therefore, we can multiply each side of the equation by the same number or expression. This is especially useful to eliminate a variable, before using the addition method. For example, suppose the equations in a system were 5x +3y = 17 and 5x-2y =-3. If they were to be added without multiplying, the new equation would be 5x +5x +3y – 2y = 17-3, or 10x-y =14. That is not closer to a solution, as there are still 2 variables in the system. Suppose both sides of the second equation are multiplied by -1, so that the new equation is -1(5x -2y) = -1(-3), or -5x +2y = 3. Using the addition method, 5x – 5x +3y +2y = 17 +3, or 5y =20, or y =4. If 5x +12 = 17, then 5x = 5, or x =1. Using the second equation to check, 5-8 = -3.

Using Multiplication More than Once

Sometimes the multiplication property needs to be used more than once in order to use the addition method. Suppose the system of equations is 5x +3y = 2 and 3x +5y =-2. Using the multiplication property once, 5(5x +3y) = 5(2) = 25x +15y = 10. The second equation can be multiplied by -3, so that -3(3x +5y) = -3(-2), or -9x -15y =6. Then the addition method can be used, so that 25x -9x +15y -15y = 10+6 or 16x = 16, or x =1. Solving for y, 3y = 2-5, or -3, so y= -1. Checking the second equation, 3 (1) + 5 (-1) = -2. The solution is (1, -1).

Problem-Solving Using the Addition Method

Suppose that the problem were to translate a word problem to a system of equations, then solve. The sum of two numbers is 115, and their difference is 21. Understanding the problem, the first equation is x +y = 115, and the second equation is x-y = 21. Using the addition method, x + x +y-y = 115 +21, or 2x =136, or x = 68. Substituting for x, 68 +y = 115, or y = 47. Checking with the second equation, 68-47 = 21.
Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Huron, SD: visit: Tutoring in Huron, SD
]]>9083Math Review of Solving Systems by Substitution
http://schooltutoring.com/help/math-review-of-solving-systems-by-substitution/
Wed, 11 Jan 2017 16:12:39 +0000http://schooltutoring.com/help/?p=9076Overview
One of the ways to solve systems of equations is by graphing the equations. However, graphing the equations is not always the most accurate method to solve them. If one variable in a system is represented in terms of the other variable in the system, the systems can be solved by substitution.

Using Substitution

Suppose one of the equations in the system is x + y = 5 and the other equation is x = y +1. The expression y +1 can be substituted for x, so that y +1 +y =5. Then, there is just one variable so that 2y +1 =5, 2y +1 -1 = 5-1, or 2y = 4, or y =2. In order to check, substitute the value of y to solve for x, such that x +2 = 5, or x +2-2 = 5-2, or x = 3. Check the second equation also, so that 3 =2 +1. That is the way to use substitution to solve a system of equations.

Isolating the Variables

Sometimes, the variables cannot be isolated as easily in a system of equations, but the system of substitution can still be used. Suppose the equations were x-2y = 8 and 2x +y = 8. The first equation can be rearranged such that x = 8 +2y. Using substitution, the second equation then becomes 2(8 +2y) +y =8, or 16 +4y +y =8. As before, there is only one variable, such that 5y = 8-16 or 5y=-8, or y = -8/5. Again, check the value of x, so that x – (2)(-8/5) =8, or x +16/5 =8. (Notice how the sign changes when two negative values are multiplied.) Then multiply both sides by 5, so that 5x +16 = 40, or 5x =24 or x = 24/5. To check the first equation, 24/5 – 2[-8/5] equals 24/5 +16/5 = 40/5, or 8. To check the second equation 2 (24/5) – (8/5) = 48/5 – 8/5) = 40/5 = 8.

Understanding the Problem and Developing a Plan

Math problems that are written in words can often be translated into systems of equations, then solved by using substitution. Suppose the statement were “The sum of two numbers is 82. One number is 12 more than the other. What is the larger number?” The first sentence can be represented by the equation x +y = 82. The second sentence can be represented by the equation x=12 +y.

Problem-Solving: Solving the Problem and Checking the Answer

To solve the problem, take the system of equations and use substitution, so that 12 +y +y = 82, then 2y = 82-12, or 2y = 70, then y = 70/2, or 35. Using the second equation to solve for x, 12 +35 = 47, and using the first equation, 47 +35 = 82.
Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Columbia, SC: visit: Tutoring in Columbia, SC]]>9076SAT Review of Multiple-Choice Questions
http://schooltutoring.com/help/sat-review-of-multiple-choice-questions/
Thu, 27 Oct 2016 23:43:51 +0000http://schooltutoring.com/help/?p=8239Overview
The SAT consists mostly of multiple-choice questions, except for the essay and some mathematics questions that require an answer grid. Each multiple-choice question has 5 alternative answers. Four of them are distractors, and one alternative is the correct answer.

Following Directions

It is very important to follow directions exactly when taking the SAT or any other standardized test. Study the directions for each type of test as part of preparation before taking the SAT. Bring several Number 2 pencils and erasers on the day of the test, and remember to fill in the bubbles on the answer sheet completely, so that the machine will read the answers that are chosen. Use the approved calculator for the math portion, and practice with it before the test so that it is familiar. The essay portion must be written legibly in pencil, so that it can be scanned.

Multiple-Choice Format

Most of the questions are in multiple-choice format, with 5 possible answers for each question. All the math questions in multiple-choice format range from easy to hard. The multiple-choice questions on the critical reading portions refer to that reading portion alone. The advantage for students using the multiple-choice format is that the correct answer is already one of the alternatives.

Eliminating Alternatives

Raw scores on the SAT are calculated so that each correct answer receives a full point, each incorrect answer subtracts ¼ of a point, and each unanswered question receives no points. That formula is supposed to discourage students from random guessing. However, students can narrow the field by eliminating distractors that are clearly incorrect. Suppose a student can confidently state that 2 of the 5 possible alternatives on a question are incorrect. The probability of getting any one of the three alternatives correct is 33%, which is already higher than the 25% incorrect-answer penalty. If 3 alternatives can be eliminated, the probability is 50%. Skillful preparation for the SAT ensures students can eliminate alternatives, and thus raise their SAT scores.

Choosing the Best Answer

Students can use their answer books as scratch paper during the test, and are encouraged to do so. That way, they can draw diagrams for geometry problems, cross out incorrect alternatives, underline key words in sentences; and do anything to help choose the best answer for every question. Students can also circle questions in the answer book that stump them, as a reminder to go back and try again if there is extra time. During SAT preparation, individual students can learn the methods and strategies to help them achieve the best scores possible on the SAT, and get into the colleges of their choice.
Interested in SAT tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academyis the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Washington, DC: visit: Tutoring in Washington, DC]]>8239Math and Physics Review of Curling and Bobsled
http://schooltutoring.com/help/math-and-physics-review-of-curling-and-bobsled/
Tue, 18 Oct 2016 01:17:53 +0000http://schooltutoring.com/help/?p=8204Overview
Curling and bobsled are winter sports that rely on friction against an icy track or surface. In curling, a special stone is moved by a combination of momentum and friction against a sheet of ice. Team players use a variety of strategies to determine which of their stones will score the highest. In bobsledding and related sports, two and 4 person teams gain maximum velocity at the start, steering their sleds to minimize the effects of gravity, wind resistance, and drag.

Curling

The sport of curling probably originated in Scotland in medieval times. Weavers used their large granite stones from warp beams to skim across the ice. They built special shallow ponds and used frozen rivers. The object of the game is to move the stone down the pond to a target, called “home.” Once the team member pushes off the block to give momentum to the stone, it is not kicked or thrown. The team captain, or “skip”, guides the stone with one broom, while two other players sweep the ice back and forth in front of the stone with special brooms, generating enough heat from friction to melt a thin film of water for the stone to glide upon. If stones collide, they exchange momentum.

Equipment for Curling

The stones weigh around 45 pounds, and are made from a type of granite that resists water, so any melting ice becomes the glide path. Absorbed water would slow the stone’s movement. At one time, curling brooms were made of corn husks, but curling brooms used today are made from synthetic materials to stand up to the rapid sweeping action across the ice.

Bobsledding

The winter sport of bobsledding calls for two or four person teams. They push an aerodynamically-designed sled down a 50 meter start course, jump into the sled, keeping it steady and straight, and careen down the course against the force of gravity. The force of gravity can reach as much as 5G, similar to the forces on fighter pilots.

Minimizing Drag and Air Resistance

After the bobsled team pushes off the sled, no further acceleration is possible, as the vehicles are not motorized. The smooth design of the bobsled, as well as the rubber surface of the suits competitors wear, are designed to minimize the amount of drag and air resistance that would slow them down.
Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academyis the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Smyrna, TN: visit: Tutoring in Smyrna, TN]]>8204Math Review of Representing Solid Figures
http://schooltutoring.com/help/math-review-of-representing-solid-figures/
Mon, 15 Aug 2016 21:55:49 +0000http://schooltutoring.com/help/?p=8183Overview
Three-dimensional solid figures can be represented by the two-dimensional pattern of polygons that create them. The pattern, called a net, is a visual representation that illustrates the formula for the surface area of the three-dimensional figure. If the net were folded, it would produce that figure.

Representation of Cylinders

The net for a cylinder consists of two circles adjoining a rectangle. This relates to the formula for the surface area of a cylinder; 2 πr^{2}+ 2πrh. The 2 πr^{2} is the formula for the area of the two circles. In order for the rectangle to fit around the circumference of the circle, the width of the rectangle is 2πr. The height of the rectangle is the height of the cylinder. Since the formula for the area of a rectangle is length multiplied by width, the area of the rectangle will have the measurement 2πrh.
Representation of Rectangular Prisms
The net for a cube consists of the six square faces that make up the cube. A square has the same length, width, and height. It is a special type of a rectangular prism, also known as a rectangular cuboid. A rectangular prism also has 6 faces, in three parallel pairs that meet at right angles. The top and bottom faces are congruent, as are the two other pairs of opposite sides. The formula for the surface area of a rectangular prism is 2(lw +wh +lh), which the net illustrates perfectly.

Representations of Pyramids

Pyramids are solid figures with triangular faces that meet at a single point called an apex, and a polygon base. A tetrahedron is a special type of pyramid with 4 triangular faces, and a regular tetrahedron, with all triangles equilateral and congruent, is a Platonic solid. Another type of pyramid has a square or rectangular base and three triangular sides. The net that illustrates the pyramids has the base bounded by triangles on each side. A regular tetrahedron has a net with all four triangles inside a larger triangle.

Representations of Other Figures

Many other solid figures can be represented by their nets. For example, a cone with a circular base is represented by the circular base adjoined by a quarter circle. Solid figures have been extrapolated into more than three dimensions. A tesseract is a four-dimensional figure with three-dimensional faces. It has been used in surreal art, science fiction, music, and popular culture.
Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.
SchoolTutoring Academyis the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Pittsburgh, PA: visit: Tutoring in Pittsburgh, PA]]>8183