Question 3

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Jambmaths question: 

The  radius of circular disc is increasing at the rate of 0.5cm/sec. At what rate is the area of the disc increasing when its radius is 6cm

Option A: 

$3\pi c{{m}^{2}}/\sec $

Option B: 

$36\pi c{{m}^{2}}/\sec $

Option C: 

$18\pi c{{m}^{2}}/\sec $

Option D: 

$6\pi c{{m}^{2}}/\sec $

Jamb Maths Solution: 

$\begin{align}  & \tfrac{dr}{dt}=0.5cm/\sec ,\text{  }A=\pi {{r}^{2}},\text{  }\frac{dA}{dr}=2\pi r \\ & \frac{dA}{dt}=\frac{dA}{dr}\times \frac{dr}{dt}=2\pi r\times 0.5=\pi r \\ & \text{when }r=6cm \\ & \frac{dA}{dt}=6\pi c{{m}^{2}}/\sec  \\\end{align}$

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