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Question

A tent of height 77 dm is in the form of a right circular cylinder of diameter 36 m and height 44 dm surmounted by a right circular cone. Find the cost of the canvas at Rs. 3.50 per square meter.

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Solution

The radius of cylinder and radius of cone both will be equal to 18 m.

As we know that,
1 m=10 dm
So, 1 dm=0.1 m

Therefore,
Height of the tent =77 dm
=77×0.1 m
=7.7 m

Height of cylinder =44 dm
=44×0.1 m
=4.4 m

Height of cone =7.74.4
=3.3m

The slant height of the cone can be calculated by using height and the radius of the cone,
l=R2+H2=(18)2+(3.3)2=324+10.89=334.89=18.3 m

Total surface area of tent =πRl+2πRHcylinder
=πR(l+2Hcylinder)
=π×18(18.3+2×4.4)
=18π×27.1
=1532.46 m2

The total cost of canvas = Cost of canvas per square meter × Surface area of the tent in square meters
=1532.46×3.5
=Rs. 5363.64

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