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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