The height of a right circular cylinder is $10.5\ m$. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder.

 Given:

The height of a right circular cylinder is $10.5\ m$. Three times the sum of the areas of its two circular faces is twice the area of the curved surface.

To do:

We have to find the volume of the cylinder.

Solution:

Height of the right circular cylinder $= 10.5\ m$

According to the question,

$3 \times$ sum of areas of two circular faces $= 2 \times$ area of curved surface

Let $r$ be that radius of the cylinder.

$3 \times 2 \pi r^{2}=2 \times 2 \pi r h$

$6 \pi r^{2}=4 \pi r h$

$3 r=2 h$

$3r=2 \times 10.5$

$3r=21$

$r=7 \mathrm{~m}$

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

$=\frac{22}{7} \times 7 \times 7 \times 10.5$

$=1617 \mathrm{~m}^{3}$

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Updated on: 10-Oct-2022

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