The height of a cylinder is $14 c m$ and its $C S A$ is $264 {c m}^{2},$ then cylinder is......... ${c m}^{3}$

183

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396

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896

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968

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Solution

The correct option is D $396$
$F o r m u l a u s e d$
$C S A o f c y l i n d e r = 2 π r h$
$V o l u m e o f c y l i n d e r = π r^{2} h$
$G i v e n$
$h e i g h t = 14 c m$
$C S A = 264 c m^{2}$
$2 π r h = 264$
$\Rightarrow 2 \times \frac{22}{7} \times r \times 14 = 264$
$\Rightarrow r = \frac{264 \times 7}{2 \times 22 \times 14} = 3 c m$
$V o l u m e = π r^{2} h$
$= \frac{22}{7} \times {(3)}^{2} \times 14$
$= \frac{22 \times 9 \times 14}{7}$
$= 396 c m^{3}$

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