Question 36

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Jambmaths question: 

If the volume of hemisphere is increasing at a steady rate of 18πm3s–1 . At what rate is its radius changing when it is 6m

Option A: 

2.50ms–1

Option B: 

2.00 ms–1

Option C: 

0.25 ms–1

Option D: 

0.20 ms–1

Jamb Maths Solution: 

$\begin{align}  & V=\tfrac{2}{3}\pi {{r}^{3}} \\ & \frac{dV}{dt}=18\pi {{m}^{3}}{{s}^{-1}} \\ & \frac{dV}{dr}=2\pi {{r}^{2}},\text{  }\frac{dr}{dV}=\frac{1}{2\pi {{r}^{2}}} \\ & \frac{dr}{dt}=\frac{dV}{dr}\times \frac{dV}{dt}=\frac{1}{2\pi {{r}^{2}}}\times 18\pi  \\ & \frac{dr}{dt}=\frac{9}{{{r}^{2}}} \\ & \text{when }r=6m \\ & \frac{dr}{dt}=\frac{9}{36}m{{s}^{-1}}=0.25m{{s}^{-1}} \\\end{align}$

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