Question

A sphere and a right circular cyclinder 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.
$\frac{4}{3}\pi r^3$ = $\pi r^{2}h$
$\frac{4}{3}r=h$
$2r=\frac{3h}{2}$
$d=\frac{3h}{2}$
Now, let h be 100 %.
$d=\frac{3h}{2}\times 100$
So, required difference = 150% - 100% = 50%
Hence, diameter of the cylinder exceed its height by 50%.