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A cloth having an area of $165 m 2$ is shaped into the form of a conical tent of radius 5m. What is the volume of the cone?

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241.74 m 3

241.14 m 3

241.74 m 3

242.74 m 3

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Detailed Solution

Given- a cloth having an area of

165 m 2

is shaped into the form of a conical tent of radius

5 m

.
Area of the cloth =

165 m 2

.
Curved surface area of the cone will be equal to the area of cloth,

∴ π r l = 165 ⇒ 227 × 5 × l = 165 ⇒ l = 10.5 m

And,

⇒ h = l 2 − r 2 ​ ⇒ h = (10.5) 2 − (5) 2 ⇒ h = 110.25 − 25 ⇒ h = 85.25 ⇒ h = 9.23 m

Volume of conical tent = 13 π r 2 h = 13227 (5) 2 (9.23) = 5076.5 21 = 241.74 m 3

Thus, the volume of conical tent is

241.74 m 3

.
Hence, option 3 is the correct option.

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