The sum of the radius of base and height of a solid right circular cylinder is \( 37 \mathrm{~cm} \). If the total surface area of the solid cylinder is $1628\ cm^2$, find the volume of cylinder. (Use \( \pi=22 / 7 \) )

Given:

The sum of the radius of base and height of a solid right circular cylinder is \( 37 \mathrm{~cm} \).

The total surface area of the solid cylinder is $1628\ cm^2$.

To do:

We have to find the volume of the cylinder.

Solution:

Let the radius of the cylinder be $r$ and the height of the cylinder be $h$.

This implies,

$r + h = 37\ cm$...…(i)

Total surface area of the cylinder $= 1628\ cm^2$

$2 \pi r(r + h) = 1628$

$2 \pi r(37) = 1628$                   [From (i)]

$2 \pi r=\frac{1628}{37}$

$2 \times \frac{22}{7} \times r=44$

$r=\frac{44 \times 7}{2 \times 22}$

$r=7 \mathrm{~cm}$

This implies,

$7+h=37$

$h=37-7$

$h=30 \mathrm{~cm}$

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

$=\frac{22}{7} \times 7 \times 7 \times 30$

$=4620 \mathrm{~cm}^{3}$

The volume of the cylinder is $4620\ cm^3$.

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Updated on: 10-Oct-2022

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