A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs 80 per square metre. [Take π = 22/7.]
The tent is made as a combination of right circular cylinder and right circular cone on top.
Height of cylindrical part of the tent = h = 3 m
Radius of its base = r = 14 m
Curved surface area of cylindrical part of tent = 2πrh
= 2 × 22/7 × 14 × 3 m2
= 264 m2
Total height of the tent = 13.5 m
Height of conical part of the tent = total height of tent – height of cylindrical part.
Height of conical part of the tent = 13.5 – 3 m =10.5 m
Let the slant height of the conical part be l
l2 = hcone2 + r2
l2 = 10.52 + 142 = 110.25 + 196 m2 = 306.25 m2
l = 17.5 m
Curved surface area of conical part of tent = πrl
= 22/7 × 14 × 17.5 m2
= 770 m2
Total surface area of tent = Curved surface area of cylindrical part of tent + Curved surface area of conical part of tent
Total Surface area of tent = 264 m2 + 770 m2 = 1034 m2
Cloth required = Total Surface area of tent = 1034 m2
Cost of cloth = Rs 80/m2
Total cost of cloth required = Total surface area of tent × Cost of cloth
= 1034 × Rs 80
= Rs 82720
Cost of cloth required to make the tent is Rs 82720