Question

A sphere, a cylinder, and a cone are of the same radius and same height.(Radius is equal to height). Find the ratio of their volumes.

• A. 2:1:3
• B. 4:3:6
• C. 2:3:2
• D. 1:2:3

Answer 1

Answer: (A)

$4:3:1$

$\because$ Radius and heights of a Sphere, Cylinder and a cone are equal.

Let ${}^{\prime }{r}^{\prime }$ be the radius and ${}^{\prime }{h}^{\prime }$ be their heights.

It is given that, $r=h$

Now, Volume of Sphere $=\frac{4}{3}\pi r^3$

and volume of cylinder $=\pi r^{2}h=\pi r^3$

volume of cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi r^3$

∴ Ratio in their volumes $=\frac{4}{3}\pi r^3:\pi r^3:\frac{1}{3}\pi r^3$

$=\frac{4}{3}:1:\frac{1}{3}$

$=\frac{4}{3}\times 3:1\times 3:\frac{1}{3}\times 3$

$=4:3:1$