Question

The radius of a circular plate is increasing at the rate of $0.01 \,cm / sec$. When the radius is $12 \,cm$, the rate at which the area increases is (in square $cm / sec$ )

• A. $60\, \pi$
• B. $24\, \pi$
• C. $1.2\, \pi$
• D. $0.24 \,\pi$

Answer 1

Answer: (D)

$\frac{d r}{d t}=0.01\, cm / s$, when $r=12\, cm$, then $\frac{d A}{d t}=$ ?
$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(12) \cdot(0.01) $
$\Rightarrow \,\frac{24}{100} \pi$
$ \Rightarrow \,0.24 \pi$