Jambmaths question:
A circle with radius 5cm has its radius increasing at the rate of 0.2cms-1. What will be the corresponding increase in the area?
Option A:
$2\pi$
Option B:
$5\pi$
Option C:
$\pi$
Option D:
$4\pi$
Jamb Maths Solution:
$\begin{align} & r=5cm,\text{ }\frac{dr}{dt}=0.2cm{{s}^{-1}} \\ & A=\pi {{r}^{2}} \\ & \frac{dA}{dr}=2\pi r \\ & \frac{dA}{dt}=\frac{dA}{dr}\times \frac{dr}{dt} \\ & \frac{dA}{dt}=2\pi r\times 0.2=0.4\pi r \\ & \text{when }r=5cm \\ & \frac{dA}{dt}=0.4\pi \times 5=2\pi \\\end{align}$
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