Question

Find the rate of change of the volume of a cube with respect to its side s when s=10

Answer 1

Let volume of the cube be denoted by V and side by s

So V = s³

Differentiating with respect to s we get

$\frac{dV}{ds} = 3s^{2}$

$[\frac{dV}{ds}]_{s=10}= 3.(10)²=300$

Therefore the rate of change of volume with respect to its side,s is 300 unit² when s= 10.