Question

If a cylinder and a sphere are of the same radius and same height, then the ratio of their volumes is

• A. 2 : 3
• B. 3 : 2
• C. 4 : 3
• D. 5 : 4

Answer 1

The correct option is B 3 : 2

Given that the cylinder and the sphere have the same radii and height.

Let $r$ and $h$ be the radius and height of both the cylinder and sphere respectively.
Now, height of the sphere = $2r$
$\therefore h=2r$
∴ Ratio of their volumes = Volume of cylinder : Volume of sphere
$=\pi r^{2}h:\frac{4}{3}\pi r^3$
$=\pi r^2\times 2r:\frac{4}{3}\pi r^3$
$=2:\frac{4}{3}$
= 3 : 2
Hence, the correct answer is option (b).