Question

A cylinder whose height is equal to $2\frac{1}{4}$ times its diameter has the same volume as a sphere of radius 4 cm The radius of the base of the cylinder is

• A. $3\frac{1}{2}$
• B. $3$ cm
• C. $2\frac{1}{3}$
• D. $2\frac{2}{3}$

Answer 1

The correct option is D $2\frac{2}{3}$

For the cylinder,
$heighth=\frac{9}{4}Diameter=\frac{9}{2}Radius$
Given, volume of the cylinder $=$ volume of the sphere

$=>\pi \times r^2\times \frac{9}{2}r=\frac{4}{3}\pi 4^3$

$r^3=\frac{8}{27}\times 4^3$
$=>r=\frac{2}{3}\times 4=\frac{8}{3}=2\frac{2}{3}$