Case Study - 2:

A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around $250$ years back, in open fields, now generally performed in tents.

Question

Case Study - 2:

A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around $250$ years back, in open fields, now generally performed in tents.

One such 'Circus Tent' is shown below.

[IMAGE_1]

The tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of cylindrical part are $9$ m and $30$ m respectively and height of conical part is $8$ m with same diameter as that of the cylindrical part, then find

(1) the area of the canvas used in making the tent;

(2) the cost of the canvas bought for the tent at the rate Rs. $200$ per sq m, if $30$ sq m canvas was wasted during stitching.

Accepted Answer

Step 1: Cross-section diagram of tent: cylinder height 9m, cone height 8m, radius 15m, slant height l
Step 2: (1) $l = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17$ m. Area of canvas $= \pi r l + 2\pi r h = \pi r(l + 2h) = \frac{22}{7} 	imes 15(17 + 18) = 1650$ m$^2$
Step 3: (2) Canvas used $= 1650 + 30 = 1680$ m$^2$
Step 4: Cost of canvas $= 200 	imes 1680 =$ Rs. $3,36,000$

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