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The height of a cylinder is 14 cm and its curved surface area is 264 sqcm. The volume of the cylinder is ____.

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Detailed Solution

The height of a cylinder is 14 cm and its curved surface area is 264 sqcm. The volume of the cylinder is 396

c m^{3}

.
Given, the height of a cylinder is 14 cm and its curved surface area is 264

c m^{2}

.
We know that the curved surface area of a cylinder is

2 πrh

2 πrh

= 264

2 πr (14) = 264

r = \frac{264}{28 π} = 3

cm
We know that the volume of a cylinder is

π r^{2} h = π (3)^{2} 14

.
= 396

c m^{3}

So, the volume is 396

c m^{3}

.
Hence, the correct answer is approximately 396

c m^{3}

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