Question 34

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waecmaths question: 

A sphere of radius r cm has the same volume as the cylinder of radius 3cm and height 4cm. Find the value of r

Option A: 

$\tfrac {2}{3}$

Option B: 

2

Option C: 

3

Option D: 

6

waecmaths solution: 

$\begin{align}  & {{V}_{sphere}}=\tfrac{4}{3}\pi r_{sphere}^{3} \\ & {{V}_{cylinder}}=\pi r_{cylinder}^{2}h \\ & \tfrac{4}{3}\pi r_{sphere}^{3}=\pi {{(3)}^{2}}4 \\ & {{r}^{3}}=\frac{{{3}^{2}}\times 4\times 3}{4}=27 \\ & r=\sqrt[3]{27}=3 \\\end{align}$

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