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 ?

Answers (1)

Answer : 50 %

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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