Question

A stone is dropped into a quiet lake and waves move in circles at the speed of $5\, cm/sec$. At that instant, when the radius of circular wave is $8 \,cm$, how fast is the enclosed area increasing ?

• A. $87\pi\, cm^2/s$
• B. $80 \pi \,cm^2/3$
• C. $6 \pi \, cm^{2/s}$
• D. $\frac {8}{3} cm^2/s$

Answer 1

Answer: (B)

$80 \pi \,cm^2/3$

Answer 2

Given, $\frac{d r}{d t}=5\, cm / s$
$\because$ Area of circular wave, $A=\pi r^{2}$
$\Rightarrow \frac{d A}{d t}=2 \pi r \frac{d r}{d t}$
$\Rightarrow \frac{d A}{d t}=2 \pi(8) \times 5=80\, \pi\, cm ^{2} / s$