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Question

The volume of a cylinder is 504π cm3 and height is 14 cm. Find its curved surface area and total surface area. Express answer in terms of π.

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Solution

Given:
Volume of the cylinder = 504π cm3
Height (h) = 14 cm
We need to find the radius of the cylinder to find the curved surface area and total surface area of the cylinder.
We know:
Volume of a cylinder = πr2h
504π = π × r2 × 14
r2 = 36
r = 36 cm = 6 cm
Thus, we have:
Curved surface area of the cylinder = 2πrh
= 2π × 6 × 14
= 168π cm2
And,
Total surface area of the cylinder = 2πr (r + h)
= 2π × 6 × (6 + 14)
= 240π cm2

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