Question

The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 $c{m}^2$, find the volume of cylinder.

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 $c{m}^2$

⇒ 2 πr × 37 cm = 1628 $c{m}^2$
⇒ r = 7 cm

As per question, r + h = 37 cm

⇒ 7 cm + h = 37 cm

⇒ h = 37 cm – 7 cm = 30 cm

Volume of cylinder = $\pi$$r^{2}h$ = 4620 $c{m}^3$

Thus, the volume of cylinder is 4620 $c{m}^3$