Question

find the volume of a frustum of a cone of height 14 cm and radii are 10 cm and 20 CM​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Height of frustum of cone is 14 cm

• 1st Radius is 10 cm

• 2nd Radius is 20 cm

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Volume of a frustum of a cone

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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We know that ,

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$\underline{\bold{\texttt{Volume of frustum of cone :}}}$

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➠ $\sf\dfrac{ \pi h } { 3 } (R^2 + R'^2 + RR')$ ⚊⚊⚊⚊ ⓵

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Where ,

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• h = Height

• R = 1st Radius

• R' = 2nd Radius

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$\underline{\bold{\texttt{Volume of given frustum of cone :}}}$

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• h = 14 cm

• R = 10 cm

• R' = 20 cm

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf \dfrac{ \pi h } { 3 } (R^2 + R'^2 + RR')$

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➜ $\sf \dfrac { \dfrac { 22 } { 7 } \times 14} { 3 } (10^2 + 20^2 + 10(20))$

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➜ $\sf \dfrac { 22 \times 2} { 3 } (100 + 400 + 200)$

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➜ $\sf \dfrac { 44} { 3 } (700)$

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➜ $\sf \dfrac { 30800 } { 3 }$

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➨ 10266.66 cu. cm.

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• Hence the volume of frustum of cone is 10266.66 cu. cm.