A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is 10 cm.

Question

Philoid · Accepted Answer

Let V be the volume of the sphere, then

Therefore, Rate of change of volume (V) with respect to its radius (r) is given by,

…….. by chain rule

Thus, when r = 10cm

Then,

Therefore, the rate at which its volume is increasing with the radius when the later is 10 cm is 400π cm³/s.