A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.

 Given:

A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. 

To do:

We have to find the ratio of their volumes.

Solution:

Diameter of the sphere, cylinder and the cone are equal.

Let the diameter of them be $2r$

This implies,

Radius of each $= r$

Height of the cylinder $=$ diameter

$= 2r$

Height of the cone $= 2r$

Therefore,

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

Volume of the cylinder $= \pi r^2h$

$=\pi r^{2} \times 2 r$

$=2 \pi r^{3}$

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

$=\frac{1}{3} \pi r^{2} \times 2 r$

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

Ratio of their volumes $=\frac{4}{3} \pi r^{3}: 2 \pi r^{3}: \frac{2}{3} \pi r^{3}$

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

$=4: 6: 2$

$=2: 3: 1$

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Updated on: 10-Oct-2022

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