A tent of height 77dm is in the form of a right circular cylinder of diameter 36m and height 44dm 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 18m.
As we know that,
1m=10dm
So, 1dm=0.1m
Therefore,
Height of the tent =77dm
=77×0.1m
=7.7m
Height of cylinder =44dm
=44×0.1m
=4.4m
Height of cone =7.7−4.4
=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=18.3m
Total surface area of tent =πRl+2πRHcylinder
=πR(l+2Hcylinder)
=π×18(18.3+2×4.4)
=18π×27.1
=1532.46m2
The total cost of canvas = Cost of canvas per square meter × Surface area of the tent in square meters