Question

A stone is dropped into a quite lake and circular ripples are formed. Circular wave fronts move at the speed of radius increasing at the rate of $5cm/sec$. How fast is the area increasing when the radius is $10cm$ ?

• A. $80\pi c{m}^2/s$
• B. $90\pi c{m}^2/s$
• C. $85\pi c{m}^2/s$
• D. $89\pi c{m}^2/s$

Answer 1

The correct option is A $80\pi c{m}^2/s$

Enclosed area : $A=\pi r^2$
So, $\frac{dA}{dt}=2\pi r\frac{dr}{dt}$
Here $r=8cm,\frac{dr}{dt}=5cm/s$
$\Rightarrow \frac{dA}{dt}=\left(2\pi \right)\left(8\right)\left(5\right)=80\pi c{m}^2/s$