Question

The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is

• A. 2 : 1
• B. 1 : 1
• C. 2 : 3
• D. 1 : 2

Answer 1

The correct option is C

2 : 3

Let r be the radius of the sphere, then

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

Diameter of circumscribed cylinder = 2r

$\therefore Radius=r$

and height (h) = 2r

$\therefore Volume=\pi r^2\left(h\right)=\pi r^2\times 2r=2\pi r^3$

$\therefore$ Ratio between the volume of two

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

$=\frac{4}{3}:2=4:6$

$=2:3$