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Question
A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m. Find the volume of the cone.
Solution
Given: Area of the cloth to form a conical tent = 165 m2
Radius of the base of a conical tent (r) = 5 m
Now, Curved surface area of a conical tent = Area of cloth to form a conical tent
`pirl = 165`
`22/7 xx 5 xx l = 165`
`l = (165 xx 7)/(22 xx 5)`
= `(33 xx 7)/22`
= 10.5 m
Now, height of the conical tent is calculated as:
`h = sqrt(l^2 - r^2)`
= `sqrt((10.5)^2 - (5)^2`
= `sqrt(110.25 - 25)`
= `sqrt(85.25)`
= 9.23
Volume of a cone = `1/3 pir^2h`
= `1/3 xx 22/7 xx 5 xx 5 xx 9.23`
= `1/3 xx (1550 xx 9.23)/7`
= `5076.5/(7 xx 3)`
= 241.7 m3
Hence, the volume of the cone is 241.7 m3.
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