Question

a cylinder of height 72 cm and radius of base 12 cm is made up by a modeling clay a child re shapes it in the form of a cone of radius 48 cm find its height


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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 cylinder is 72 cm

• Radius of cylinder is 12 cm

• Radius of cone is 48 cm

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

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• Height of cone if both cylinder and cone are made from same clay

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

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It is given that the cylinder was of clay and is later child reshapes it into cone hence the volume of clay used in both cases would be same thus we can equate volume of cylinder to volume of cone

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$\underline{ \underline{\bold{\texttt{Volume of cylinder :}}}}$

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➠ πr²h ⚊⚊⚊⚊ ⓵

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Where ,

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• r = Radius of cylinder

• h = Height of cylinder

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$\underline{ \underline{\bold{\texttt{Volume of given cylinder :}}}}$

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• r = 12 cm

• h = 72 cm

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⟮ Putting the above values in ⓵ ⟯

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: ➜ πr²h

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: ➜ π(12)²(72) ⚊⚊⚊⚊ ⓶

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

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➠ $\sf \dfrac { 1 } { 3 } \pi (r')^2 h'$ ⚊⚊⚊⚊ ⓷

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Where ,

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• r' = Radius of cone

• h' = Height of cone

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

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• r' = 48

• h' = h'

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⟮ Putting the above values in ⓷ ⟯

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: ➜ $\sf \dfrac { 1 } { 3 } \pi (r')^2 h'$

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: ➜ $\sf \dfrac { 1 } { 3 } \pi (48)^2 h'$ ⚊⚊⚊⚊ ⓸

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As discussed above volume of cone and cylinder will remain same in this case

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Thus ,

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From equation ⓶ & ⓸

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: ➜ $\sf \pi(12)^2 (72) = \dfrac { 1 } { 3 } \pi (48)^2 h'$

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: ➜ $\footnotesize{ \sf \pi \times 12 \times 12 \times (72) = \dfrac { 1 } { 3 } \times \pi \times 48 \times 48 \times h' }$

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: ➜ $\sf \dfrac { \pi \times 12 \times 12 \times (72) } { \pi \times 48 \times 48 } = \dfrac { 1 } { 3 }\times h'$

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: ➜ $\sf \dfrac { 72 } { 4 \times 4 } = \dfrac { 1 } { 3 } \times h'$

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: ➜ $\sf \dfrac { 9} { 2 } = \dfrac { 1 } { 3 } \times h'$

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: ➜ $\sf \dfrac { 9} { 2 } \times 3 = h'$

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: ➜ $\sf \dfrac { 27} { 2 } = h'$

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: ➜ $\sf h' = 13.5 \: cm$

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• Hence the height of cone is 13.5 cm