The sum of the radius of the base and height of a solid cylinder is $37\ m$. If the total surface area of the solid cylinder is $1628\ m^2$. Find the volume of the cylinder.

 Given:

The sum of the radius of the base and height of a solid cylinder is $37\ m$.

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

To do:

We have to find the volume of the cylinder.

Solution:

Sum of the radius and the height of the cylinder $= 37\ m$

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

This implies,

$r + h = 37\ m$...…(i)

Total surface area of the solid cylinder $= 1628\ m^3$

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

$\frac{2 \times 22}{7} r(37)=1628$

$r=\frac{1628 \times 7}{2 \times 22 \times 37}$

$r=7 \mathrm{~m}$

This implies,

$h=37-r$

$=37-7$

$=30 \mathrm{~m}$

Volume $=\pi r^{2} h$

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

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

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Updated on: 10-Oct-2022

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