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The lateral surface area of a cylinder of length $14 m$ is $220 m^{2}$ . Find the volume of the cylinder.

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205 m^{3}

270 m^{3}

200 m^{3}

275 m^{3}

answer is D.

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Detailed Solution

Given,
Length of the cylinder h

= 14 m

Lateral surface area

= 220 sq . m

We know that lateral surface area of the cylinder

L . S . A . = (2 πr h)

,
Put the values,

\Rightarrow 220 = 2 πr \times 14

\Rightarrow r = \frac{220}{28 π} meter

Volume of the cylinder is,

V = π r^{2} h

\Rightarrow V = π {(\frac{220}{28 π})}^{2} (14)

\Rightarrow V = π \times \frac{(220)^{2}}{(28)^{2} π^{2}} (14)

\Rightarrow V = \frac{(220)^{2}}{(28)^{2} π^{2}} (14)

\Rightarrow V = \frac{(220)^{2}}{(28)^{2} \times \frac{22}{7}}

[∵ π = \frac{22}{7}]

\Rightarrow V = \frac{2200}{2 \times 4}

\Rightarrow V = 275 m^{3}

Option 4 is correct.

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