Question

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

Answer 1

Given as the spherical balloon inflated by pumping in 900 cubic centimetres of gas per second

As to find the rate at which the radius of the balloon is increasing when the radius is 15 cm

Suppose the radius of the given spherical balloon be r cm and let V be the volume of the spherical balloon at any instant time

Now according to the given question,

The balloon is inflated by pumping 900 cubic centimetres of gas per second hence the rate of volume of the spherical balloon increases by

dV/dt = 900 cm³/sec ...(i)

As we know that the volume of the spherical balloon is V = (4/3)πr³

By applying derivative with respect to time on both sides 

From the equation (i)

Therefore when the radius is 15cm, the above equation becomes

Thus, the rate at which the radius of the balloon is increasing when the radius is 15 cm.