Question

If a sphere, a cone and a cylinder have the same heights and same radii, then the ratio of their volumes is equal to

• A. 4 : 2 : 5
• B. 2 : 1 : 4
• C. 3 : 2 : 4
• D. 2 : 1 : 3

Answer 1

The correct option is D 2 : 1 : 3

Let the radii of a sphere, a cone and a cylinder be $r$ and their heights be $h$.

∴ $h=2r$ …..(i)


Volume of sphere $=\frac{4}{3}\pi r^3$
Volume of cone $=\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\pi r^2\times 2r$ [From (i)]
$=\frac{2}{3}\pi r^3$
Volume of cylinder $=\pi r^{2}h$
$=\pi r^2\times 2r$
$=2\pi r^3$
∴ Ratio of their volumes
= Volume of sphere : Volume of cone : Volume of cylinder
$=\frac{4}{3}\pi r^3:\frac{2}{3}\pi r^3:2\pi r^3$
$=\frac{2}{3}:\frac{1}{3}:1$
= $2:1:3$
Hence, the correct answer is option (d).