A tent is in the shape of a right circular cylinder up to a height of

1.	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]
Answer» 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 Total height of the tent = 13.5 m Curved surface area of cylindrical part of tent = 2πrh = 2 × 22/7 × 14 × 3 = 264 m² 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 = h² + r² (used cone height) = 110.25 + 196 = 306.25 or l = 17.5 m Curved surface area of conical part of tent = πrl = 22/7 × 14 × 17.5 = 770 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 + 770 = 1034 m² Cloth required = Total Surface area of tent = 1034 m² Cost of cloth = Rs 80/m² (given) 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

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]

Answer»

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

Total height of the tent = 13.5 m

Curved surface area of cylindrical part of tent = 2πrh

= 2 × 22/7 × 14 × 3

= 264 m²

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 = h² + r² (used cone height)

= 110.25 + 196

= 306.25

or l = 17.5 m

Curved surface area of conical part of tent = πrl

= 22/7 × 14 × 17.5

= 770

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 + 770

= 1034 m²

Cloth required = Total Surface area of tent = 1034 m²

Cost of cloth = Rs 80/m² (given)

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