Question

the height and base diameter of a conical tent is 16m and 24mrespectivelyfind the cost of canvas require to make at rate of 210per m​

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 conical tent is 16 m

• Diameter of conical tent is 24 m

• Rate of canvas is 210 per m

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

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• The cost of canvas require to make the tent at rate of Rs 210 per m

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

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• To find the convas used to make tent we need to calculate the surface area of cone

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$\underline{\bold{\texttt{Curved surface area of cone :}}}$

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➠ π r l ⚊⚊⚊⚊ ⓵

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Where ,

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• r = Radius of base of cone

• l = Slant height

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➠ $\sf Radius = \dfrac { Diameter } { 2 }$

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➜ Radius of base of cone = $\sf \dfrac { 24 } { 2 }$

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• Radius of base of cone = 12 m

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Now we need to find the slant height of cone

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➜ $\sf l = \sqrt { h ^2 + r ^2 }$ ⚊⚊⚊⚊ ⓶

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Where ,

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• l = Slant height

• h = Height

• r = Radius of base of cone

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Given that , h = 16 & r = 12

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⟮ Putting these values in ⓶ ⟯

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➜ $\sf l = \sqrt { 16^2 + 12^2 }$

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➜ $\sf l = \sqrt { 256 + 144}$

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➜ $\sf l = \sqrt { 400}$

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➜ l = 20 m ⚊⚊⚊⚊ ⓷

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• Hence the slant height is 20 m

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$\underline{\bold{\texttt{Curved surface area of given conical tent :}}}$

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• r = 12

• l = 20

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⟮ Putting the above values in ⓵ ⟯

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➜ π r l

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➜ π (12) (20)

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➜ 240π

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$\underline{\bold{\texttt{Cost of canvas :}}}$

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Curved surface area × Rate of canvas

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➜ 240π × 210

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➜ $\sf 240 \times \dfrac { 22 } { 7 } \times 210$

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➜ $\sf 240 \times 22 \times 30$

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➨ Rs 158400

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• Hence the cost of canvas is Rs 158400

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Additional information

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Volume of cone

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• $\sf \dfrac { 1 } { 3 } \pi r ^2 h$

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Where ,

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➻ r = Radius of base

➻ h = Height

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Total surface area of cone

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• πr(l + r)

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Where ,

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➻ l = Slant height

➻ r = Radius of base