The height of a cylinder is 20 cm. The lateral surface area is 1760 cm². What is its volume?

Question

Accepted Answer

Given:
Height (h) = 20 cm
Lateral Surface Area (LSA) = 1760 cm²

The formula for the lateral surface area of a cylinder is:
LSA = 2πrh

Substitute the given values:
1760 = 2 × π × r × 20
1760 = 40πr
r = 1760 / (40π)

Take π = 22/7:
r = 1760 / (40 × 22/7)
r = 1760 × 7 / (40 × 22)
r = 12320 / 880
r = 14 cm

Now, the volume of a cylinder is:
Volume = πr²h
= (22/7) × (14)² × 20
= (22/7) × 196 × 20
= (22/7) × 3920
= (22 × 3920) / 7
= 86240 / 7
= 12320 cm³

Thus, the volume of the cylinder is 12320 cm³.

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