Question

The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be ______ 

Options

• πcm²/s

• 2πcm²/s

• 10πcm²/s

• 60π cm²/sec

Answer 1

The radius of a circle is increasing uniformly at the rate of 2.5cm/sec. The rate of increase in the area when the radius is 12cm, will be 60π cm²/sec.

Explanation:

`(dr)/dt = 2.5`

A = `pir^2 ⇒ (dA)/dt = 2pir (dr)/dt`

⇒ `((dA)/dt)_{r = 12} = 2pi xx 12 xx 2.5` = 60π cm²/sec