Volume is the space enclosed by a three-dimensional object. When calculating volume, you are calculating the number of cubic units that object can hold inside.
Cube
Volume = s3 = s x s x s
Where s is the length of the side of the cube
Example: A cube with side lengths of 4 cm
V = s3
= 43
= 64 cm3
Rectangular Prism
Volume = l x w x h
Where l is the length, w is the width and h is the height of the prism
Example: A rectangular prism with a length of 4 cm, width of 2 cm and height of 3 cm
V= l x w x h
= 4 x 2 x 3
= 24 cm3
Cylinder
Volume = area of base x h
Where h is the height of the cylinder
Since the base of a cylinder is a circle, the area of the base is equal to pi x r2
Where r is the radius of the circle
Example: A cylinder with a height of 5 cm and a radius of 3 cm
V = area of base x h
= pi x r2 x h
= 3.14 x 32 x 5
= 141.3 cm3
Sphere
Volume = 4/3 x pi x r3
Where r is the radius of the sphere
Example: A sphere with a radius of 6 cm
V = 4/3 x pi x r3
= 4/3 x 3.14 x 63
= 904.32 cm3
Cone
Volume = 1/3 x pi x r2 x h
Where r is the radius of the circle at the base and h is the height of the cone (distance from base to tip)
Example: A cone with a height of 6 cm and radius of 3 cm
V = 1/3 x pi x r2 x h
= 1/3 x 3.14 x 32 x 6
= 56.52 cm3
Pyramid
Volume = 1/3 x area of base x h
Where h is the height of the pyramid
Note: The shapes of the bases differ depending on the type of pyramid (ie. Square-based pyramid vs. triangle-based pyramid)
Example: A pyramid with a base area of 25 cm2 and a height of 7 cm
V = 1/3 x area of base x h
= 1/3 x 25 x 7
= 58.3 cm3
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This article was written for you by Samantha, one of the tutors with SchoolTutoring Academy.