Question

Find the approximate change in volume V of a cube of side x meters caused by increasing side by 1%.

Answer 1

The volume of a cube (V) of side x is given by V=x3.

=dv=($\frac{dv}{dx}$)Δx

=(3x2)Δx

=(3x2)(0.01x) [as%of x is 0.01x]

Hence, the approximate change in the volume of the cube is 0.03x3 m3.