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.
Solution
adius of the cylinder = 14 m
Radius of the base of the cone = 14 m
Height of the cylinder (h) = 3 m
Total height of the tent = 13.5 m
Surface area of the cylinder =`2pirh =(2xx22/7xx14xx3)m^2 = 264 m^2`
Height of the cone= Total height - Height of cone = (13.5 - 3)m =10.5 m
`"surface area of the cone" = pirsqrt(r^2 + h^2)`
`pirsqrt(r^2 + h^2) = (22/7xx14xx sqrt(14^2 + 10.5^2)) m^2`
`=(44xxsqrt(196 + 110.25)) m^2 =(44xxsqrt(14^2 + 10.5^2 ))`
`= (44xx 17.5)` m2 = 770 m2
Total surface area = (264 + 770 ) m2 = 1034 m2`
`cost of cloth = Rs 1034 × 80 = Rs 82720`
