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  • A conical tent is to accommodate 11 persons . Each persons must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breath . Find the height of the cone .

A conical tent is to accommodate 11 persons . Each persons must have 4 sq. metres of the space on the ground and 20 cubic metres of air to breath . Find the height of the cone .

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 Solution:  Let h metres be the height , r metres the radius of base of the cone . Since the tent can accommodate 11 persons and each person requires 4 sq. metres of the space on the ground and 20 cubic metres of air . Therefore, 

               Area of the base =(11 imes4)m^2=44m^2Rightarrow pi r^2=44m^2......................(1)

               Volume of the cone =(11 imes20)m^3=220m^3Rightarrow frac13pi r^2h=220m^3.................(2)

Dividing (2) by (1) , we get 

               fracfrac13pi r^2hpi r^2=frac22044Rightarrow frach3=5Rightarrow h=15m.

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Deependra Verma

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