Question

The volume of a spherical balloon is increasing at the rate of 10 cubic centimetre per minute. The rate of change of the surface of the balloon at the instant when its radius is 4 centimetres, is ______

Options

• `5/2` cm²/min 

• 5 cm²/min 

• 10 cm²/min 

• 20 cm²/min 

Answer 1

The volume of a spherical balloon is increasing at the rate of 10 cubic centimetres per minute. The rate of change of the surface of the balloon at the instant when its radius is 4 centimetres, is 5 cm²/min.

Explanation:

Here, V = `4/3pir^3` and S = 4πr²

⇒ `(dV)/dt = 4pir^2 (dr)/dt ⇒ (dr)/dt = 10/(4pir^2) = 5/(32pi)`

∴ `(dS)/dt = 8pir (dr)/dt`

= `8pi xx 4 xx 5/(32pi)` = 5 cm²/min