SSC Sample Paper Mock Test-11 SSC CGL Tear-II Paper-1

The volumes of a sphere and a right circular cylinder having the same radius are equal. The ratio of the diameter of the sphere to the height of the cylinder is

A) 3 : 2

B) 2 : 3

C) 1 : 2

D) 2 : 1

Correct Answer: A

Solution :

Volume of sphere \[=\frac{4}{3}\pi {{r}^{3}}\]

Volume of cylinder \[=\pi {{r}^{2}}h\]

As given, \[\pi {{r}^{2}}h=\frac{4}{3}\pi {{r}^{3}}\]\[\Rightarrow \]\[h=\frac{4}{3}r\]

\[\Rightarrow \] \[\frac{h}{r}=\frac{4}{3}\]

\[\Rightarrow \] \[\frac{h}{2r}=\frac{4}{3\times 2}=\frac{2}{3}\]

\[\therefore \] \[\frac{d}{h}=\frac{3}{2}\] [where d = 2r]