Find the height of the cylinder whose radius is 7 cm and the total surface area is 1100 cm².

Given:

Radius of the cylinder = 7 cm

Total surface area of the cylinder = 1100 cm²

Let h be the height of the cylinder.

The total surface area of cylinder = 2πr(r + h)

$⇒ 2 \times \dfrac{22}{7} \times 7 (7 + h) = 1100\\[1em] ⇒ \dfrac{44}{\cancel{7}} \times \cancel{7} (7 + h) = 1100\\[1em] ⇒ 44 \times (7 + h) = 1100\\[1em] ⇒ 7 + h = \dfrac{1100}{44}\\[1em] ⇒ 7 + h = 25\\[1em] ⇒ h = 25 - 7\\[1em] ⇒ h = 18$

Hence, the height of the cylinder is 18 cm.