# A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceeds its height ?

Let radius of sphere be r, radius of cylinder be R, height of cylinder be H

Volume of sphere $\left ( \frac{4}{3}\pi r^{3} \right )$ = Volume of cylinder $\left ( \pi R^{2}H \right )$

Now, it is given that r = R

$\left ( \frac{4}{3}\pi r^{3} \right )=\left ( \pi r^{2}H \right )$

$\frac{4}{3}r=h$

$4r=3h$

$2(2r)=3h$                                      $\left ( \therefore d=2r \right )$

$\Rightarrow 2d=3h$

$d=1.5 h=\left ( 1+0.5 \right )h$

$d=\left ( 1+\frac{50}{100} \right )h$

The diameter exceeds the height by 50%.

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