Question

a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and the diameter of a cylindrical part are 2.1 M and 4m and slant height of conical part is 2.8 M .find the cost of Canvas needed to make the tent if the Canvas is available at the rate of ₹ 500 per square metre. also find the volume of air enclosed in the tent.

Answer 1

Answer:

Rs. 22,000

Step-by-step explanation:

Area of Canvas = Curved area of cone + Curved surface area of cylinder

Curved Surface area of Cone:

Diameter of cone = Diameter of cylinder = 4 m.

So, Radius = Diameter / 2 = 4/2 = 2 m.  Slant Height = 2.8 m.

Curved surface area of cone = πrl

                                                 = 22/7 *2 * 2.8 = 17.6 m².

Curved Surface area of Cylinder:

Diameter of cone = Diameter of cylinder = 4 m.

So, Radius = Diameter / 2 = 4/2 = 2 m.  Height = 2.1 m.

Curved surface area of cylinder = 2πrh = 2 * 22/7 * 2 * 2.1

                                                                = 26.4 m².

Area of Canvas = Curved area of cone + Curved surface area of cylinder

                           = 17.6 + 26.4

                           = 44 m².

Now, Cost of Canvas of tent for 1 m² = Rs. 500.

Cost of Canvas of tent for 44 m² = 44 * 500 = Rs. 22,000.

Answer 2

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Given:

Height (h) of the cylindrical part = 2.1 m

Diameter of the cylindrical part = 4 m

Radius of the cylindrical part = 2 m

Slant height (l) of conical part = 2.8 m

Area of canvas used = CSA of conical part + CSA of cylindrical part

=πrl+2πrh

=π×2×2.8+2π×2×2.1

=2π[2.8+4.2]

=2× 22/7

=44m

Cost of 1 m²

canvas =500 rupees

Cost of 44 m²

canvas =44×500=22000 rupees.

Therefore, it will cost 22000 rupees for making such a tent.