Question

A stone is dropped into a quiet lake and waves move in a circle at a speed of $3.5cm/sec$. At the instant when the radius of the circular wave is $7.5cm$. The enclosed area increases as fastly as.

• A. $52.5\pi$ $c{m}^2/sec$
• B. $50.5\pi$ $c{m}^2/sec$
• C. $57.5\pi$ $c{m}^2/sec$
• D. $62.5\pi$ $c{m}^2/sec$

Answer 1

The correct option is A $52.5\pi$ $c{m}^2/sec$

Given $r=7.5cm$ ,$\frac{dr}{dt}=3.5cm/sec$
$A=\pi r^2$
$\frac{dA}{dt}=2\pi r\times \frac{dr}{dt}$
$\frac{dA}{dt}=2\pi \times 7.5\times 3.5$
$\frac{dA}{dt}=52.5\pi c{m}^2/sec$