Question

A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m² of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 500 per m².

Answer 1

Radius of the cylindrical tent (r) = 14 m

Total height of the tent = 13.5 m

Height of the cylinder = 3 m

Height of the conical part = 10.5 m

Slant height of the cone (l) = `sqrt(h^2 + r^2)`

= `sqrt((10.5)^2 + (14)^2`

= `sqrt(110.25 + 196)`

= `sqrt(306.25)`

= 17.5 m

Curved surface area of cylindrical portion

= 2πrh

= `2 xx 22/7 xx 14 xx 3`

= 264 m²

Curved surface area of conical portion

= πrl

= `22/7 xx 14 xx 17.5`

= 770 m²

Total curved surface area = 264 m² + 770 m² = 1034 m²

Provision for stitching and wastage = 26 m²

Area of canvas to be purchased = 1060 m²

Cost of canvas = Rate × Surface area

= 500 × 1060

= ₹ 5,30,000/-