Question

What is the ratio of volume of a sphere to volume of cylinder with an equivalent radius and height equal to the diameter?

• A. $\frac{2}{3}$
• B. $\frac{3}{4}$
• C. $\frac{1}{3}$
• D. $\frac{1}{2}$

Answer 1

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

Volume of sphere of radius 'r' = $\frac{4}{3}\pi r^3$
Volume of a cylinder of radius 'r' and height '2r' = $\pi r^2\left(2r\right)$ = $2\pi r^3$

$\therefore$ Required ratio = $\frac{Volumeofsphere}{Volumeofcylinder}$
= $\frac{\frac{4}{3}\pi r^3}{2\pi r^3}$
= $\frac{2}{3}$