Question 11

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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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