A balloon, which always remains spherical, has a variable radius . Determine the rate of change of volume with respect to its radius when the radius is 10 cm. .

Explanation

The volume of a sphere (V) with radius (r) is given by `V=frac{4}{3} pi r^{3}`

Rate of change of volume (V) with respect to its radius (r) is given by,
Therefore, when radius = 10 cm,
` frac{dV}{dr}=4 pi(10)^{2}= 400pi`

Hence, the volume of the balloon is increasing at the rate of`400 pi cm^{2}.`