Question

The sum of height and radius of the base of a solid cylinder is $37cm$. Total surface area f the cylinder is $1628c{m}^2$, Find its volume of the cylinder.

Answer 1

Let '$h$' be height & '$r$' be radius of the base of cylinder.

Also, given that $r+h=37\text{cm}$ ------(1)

and TSA of cylinder = $1628{\text{cm}}^2$ ----(2)

we know TSA of the cylinder = $2\pi r(h+r)$

So,

$1628=2\pi r\left(37\right)$

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

$r=\frac{814}{37\pi }$

$r=7\text{cm}$

From equation (1), $r+h=37$

$7+h=37$

$h=30\text{cm}$

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

$=3.14\times 49\times 30$

$=46150.8{\text{cm}}^2$