The length of outer and inner diameter of hollow right circular cylinder are 16 cm and 12 cm respectively. Height of cylinder is 36 cm. Let us calculate how many solid cylinders of 2 cm diameter and 6 cm length may be obtained by melting this cylinder.

Given:

The length of the outer and inner diameter of a hollow right circular cylinder are 16 cm and 12 cm respectively. The height of the cylinder is 36 cm. 

To do:

We have to find the number of small cylinders obtained by melting this cylinder.
Solution:

Outer radius of the hollow cylinder $=\frac{Outer\ diameter}{2}=\frac{16}{2}=8\ cm$

Inner radius of the hollow cylinder $=\frac{Inner\ diameter}{2}=\frac{12}{2}=6\ cm$
Height of the cylinder $=36\ cm$

Volume of the hollow cylinder $=\pi (8^2-6^2)\times36$

$=\pi \times(64-36)\times36$

$=\pi \times 28\times36$

$=1008\pi$

Radius of each small cylinder $=\frac{Diameter}{2}=\frac{2}{2}=1\ cm$

Height of each small cylinder $=6\ cm$

Volume of each small cylinder $=\pi \times 1^2\times 6$

$=6\pi$

Number of small solid cylinders obtained by melting the hollow cylinder $=\frac{Volume\ of\ the\ hollow\ cylinder}{Volume\ of\ each\ small\ cylinder}$

$=\frac{1008\pi}{6\pi}$

$=168$

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Updated on: 10-Oct-2022

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