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.

Answer 1

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.