A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15 cm.

Question

Philoid · Accepted Answer

Let V be the volume of the sphere, then

Therefore, Rate of change of volume (V) with respect to time (t) is given by,

…….. by chain rule

It is given that

Then,

Thus, when r = 15cm

Then,

Therefore, the rate at which the radius of the balloon increases when the radius is 15 cm is cm/s.