Question

The sum of the radius of the base and the height of a solid cylinder is 37 metres. If the total surface area of the cylinder be 1628 sq metres, find its volume.

Answer 1

Let r and h be the radius and height of the solid cylinder respectively.

Given, r + h = 37 cm

Total surface area of the cylinder = 1628 $c{m}^2$ (Given)

∴ 2 πr (r + h) = 1628
⇒ 2 πr × 37 = 1628
⇒ r = 7 cm

Now, r + h = 37 cm
⇒7 + h = 37
⇒ h = 37 – 7 = 30 cm

Volume of the cylinder = $\pi r^{2}h=\frac{22}{7}\times 7^2\times 30=4620c{m}^3$