The subject of the formula is the variable which is on the left hand side of the formula. The subject of the formula can be changed using algebraic operations. Equations with different subjects can be derived using a single formula. We can make any variable of the formula into its subject.
The process of changing the subject of the formula is shown through the following examples.
Example 1:
Write the volume of cuboid formula with its length as its subject.
Solution:
Volume of the cube, V = length * width * height = l * w * h.
So, V = lbh
Dividing both sides of the equation by bh, we get
V/bh = l
Or l = V/bh is the formula for length.
Example 2:
What is the formula for radius ‘r’ of a sphere given that its volume V is four-third of the product of pi, square of ‘r‘ and its height ‘h’?
Solution:
Volume of sphere, V= 4/3 * π * r2 * h
3V = π * r2 * h
r2=3V/ πh
r=√ 3V/ πh is the formula for the radius ‘r’.
Substitution:
The value of the subject of the formula can be obtained by substituting all the values of the variables on the right side. The process of substituting the values of the variables is shown through the following example.
Example:
Given the volume of a cylinder, V=πr2h, What is the value of V at π=3.14, r = 2.8 cm and h = 5cm?
Solution:
V = πr2h = 3.14 * 2.8 * 2.8 * 5 = 123.088 cm2
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