If the volume of a cylinder of height 7 cm is 448 π cm 3 , find its lateral surface area and total surface area.

Mathematics

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Volume of cylinder = πr²h.

Given, Volume of cylinder = 448 π cm³ and height = 7 cm.

∴ πr²h = 448 π
⇒ r²h = 448 (Dividing both sides by π)
⇒ r² × 7 = 448
⇒ r² = $\dfrac{448}{7}$
⇒ r² = 64
⇒ r = $\sqrt{64}$ = 8 cm.

Lateral surface area of cylinder = 2πrh = 2π × 8 × 7 = 112π cm².

Total surface area = 2πr(h + r) = 2π × 8 × (8 + 7) = 2π × 8 × 15 = 240π cm².

Hence, the lateral surface area of cylinder = 112π cm² and total surface area = 240π cm².

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