Q. 34.7( 6 Votes )

A tent is of the shape of a right circular cylinder up to a height of 3 m and then becomes a right circular cone with a maximum height of 13.5 m above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs 2 per square metre, if the radius of the base is 14 m.

Answer :

Given: Height of cylinder “h” = 3 m


Radius “r” = 14 m


Height of tent “H” = 13.5 m


Cost of painting = Rs 2 per m2


Formula Used:


Curved surface area of cylinder = 2πrh


Curved surface area of cone = πrl


Explanation:



We have, r = 14 m


h = 3 m


CSA of cylinder = 2πrh



= 264 m2


The height of the cone = Height of tent – height of cylinder


= 13.5 – 3


= 10.5 m


Now slant height of the cone is


Where r = 14 m and h = 10.5 m






We have shown, how to take square-root



l = 17.5 m


So CSA of cone = π r l



= 770 m2


Total area to be painted = CSA of the cylinder + CSA of the cone


= 264 m2 + 770 m2


= 1034 m2


Cost of painting 1 m2 = Rs 2


Cost of painting 1034 m2 = Rs 2 × 1034


= Rs 2068


Hence cost of painting the tent is Rs 2068.


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