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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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