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 ₹ 500 per m². (Note that the base of the tent will not be covered with canvas.)

Given,

Diameter of cylindrical part (d) = 4 m

Radius of cylindrical part = $\dfrac{d}{2} = \dfrac{4}{2}$ = 2 m,

Height of cylindrical part (h) = 2.1 m

Slant height of conical part (l) = 2.8 m

From figure,

Radius of conical part = Radius of cylindrical part = r = 2 m.

Area of canvas for making tent = Curved surface area of conical part + Curved surface area of cylindrical portion

= πrl + 2πrh

= πr(l + 2h)

= $\dfrac{22}{7} \times 2 \times (2.8 + 2 \times 2.1)$

= $\dfrac{44}{7} \times (2.8 + 4.2)$

= $\dfrac{44}{7} \times 7$

= 44 m².

Cost of canvas = Area of canvas required × Cost per square units

= 44 × 500

= ₹ 22000.

Hence, area of canvas required for making tent = 44 m² and cost of canvas = ₹ 22000.