Question

a circus tent is in the form of right circular cylinder and right circular cone above its the diameter and height of cylindrical part of the 10th or 126 M and 5 M respectively the total height of the tent is 21 m.find the total cost of tent if the canvas used costs rupees 12per m square

Answer 1

The total cost of the tent if the canvas used costs rupees 12 per m square is Rs. 1,78,200.

Step-by-step explanation:

Referring to the figure attached below, lets make some assumptions,

AD = total height of the tent = 21 m

BD = the height of the cylindrical part of the tent = 5 m

∴ AB = the height of the conical part of the tent = 21 - 5 = 16 m

The diameter of the base of the tent, d = 126 m

So, the radius of the base of the tent, r = 126/2 = 63 m

Step 1:

The slant height of the cone is given by,

l = $\sqrt{h^2 + r^2} = \sqrt{16^2 + 63^2} = \sqrt{256 + 3969} = \sqrt{4225} = 65 m$

We know that,

The total canvas used in making the tent is given by,

= Total curved surface area of the tent

= [Curved surface area of cylindrical part] + [Curved surface area of conical part]

= [2πrh] + [πrl]

= [2 × (22/7) × 63 × 5] + [(22/7) × 63 × 65]

= [1980 m²] + [12870 m²]

= 14850 m²

Step 2:

Now,

The cost of the canvas is given as Rs. 12 per metre square.

Therefore,

The total cost the tent with the required area of canvas i.e., 14850 m² is,

= 14850 m² * Rs. 12

= Rs. 1,78,200

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