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)` m^{2 }= 770 m^{2 }

Total surface area = (264 + 770 ) m^{2} = 1034 m2`

`cost of cloth = Rs 1034 × 80 = Rs 82720`