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$\large{\blue{➢{\underline\color{maroon}{\sf{Question :-}}}}}$
The radius and height of a cylinder are in the ratio 3:2 .If its Volume is 19404 cm² .Find the radius and height .



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Answer 1

Answer:

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Answer 2

$\huge{ \boxed{ \red{ \pmb{ \sf \: Given:-}}}}$

• The radius and height of a cylinder are in the ratio 3:2 .
• Volume is 19404 cm² .

$\huge{ \boxed{ \red{ \pmb{ \sf \: To \: find:-}}}}$

• Find the radius and height.

$\huge{ \boxed{ \red{ \pmb{ \sf \: Solution:-}}}}$

The radius and height of a cylinder are in the ratio 3 : 2.

Let the radius be 3x and height be 2x.

Then,

$\tt \: Area \: of \: cylinder= 19404 \: cm^3$

$\tt \leadsto \pi {r}^{2} h = 19404$

$\tt \leadsto 19404 = \frac{22}{7} \times {(3x) }^{2} \times (2x)$

$\tt \leadsto 19404 = \frac{22}{7} \times {9x}^{2} \times 2x$

$\tt \leadsto 19404 = \frac{22 \times 18 {x}^{3} }{7}$

$\tt \leadsto 19404 = \frac{396 {x}^{3} }{7}$

$\tt \leadsto {x}^{3} = 343$

$\tt \leadsto x = \sqrt[3]{343}$

$\tt \leadsto x = 7 \: cm$

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★ Radius of cylinder

$\tt \longrightarrow 3 x$

$\tt \longrightarrow 3 \times 7$

$\tt \longrightarrow 21 \: cm$

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★ Height of cylinder

$\tt \longrightarrow 2x$

$\tt \longrightarrow 2 \times 7$

$\tt \longrightarrow 14 \: cm$