Question

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

Answer 1

Given sphere and a right circular cyclinder of the same radius.

Volume of Sphere $=\frac{4}{3}\pi r^3$

Volume of right circular cyclinder $=\pi r^{2}h$

Given Volume of Sphere = Volume of right circular cyclinder.

$\frac{4}{3}\pi r^3=\pi r^{2}h$

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

$2r=\frac{3h}{2}$

$\therefore d=\frac{3h}{2}$

Now, let h be 100 %.

D $=\frac{3h}{2}=\frac{3}{2}\times 100\%$ = $150\%$

So, required difference = $150\%-100\%=50\%$

Hence, diameter of the cylinder exceed its height by $50\%$.