A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m² . (Note that the base of the tent will not covered with canvas).

We have,

Height of the cylinderical part = 2.1 m

Diameter of the cylinderal part = 4 m

Radius of the cylinerical part = 2 m

Slant height of the conical part = 2.8 m

Thus, Total canvas used = Curved surface area of cylinder + Curved surface area of cone

\( = \ 2 \pi rh \ + \ \pi rl \ = \ \pi r(2h \ + \ l) \)

\(= \ \frac{22}{7} \ × \ 2 \ × \ (2 \ × \ 2.1 \ + \ 2.8) \ \)
\( = \ 44 \) m²

Now, cost of 1 m² the canvas for the tent = Rs 500

So, cost of 44 m² the canvas for the tent = Rs 44 × 500 = Rs 22000