Question

Read the following passage and answer the questions given below.

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. 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 ₹ 200 per sq m, if 30 sq m canvas was wasted during stitching.

Answer 1

According to given information, we have the following figure.

Clearly, the radius of conical part = radius of cylindrical part = `30/2` = 15 m = r  ...(say)

Let h and H be the height of conical and cylindrical part respectively.

Then h = 8 m and H = 9 m

∴ l = `sqrt(r^2 + h^2)`

= `sqrt((15)^2 + 8^2)`

= `sqrt(225 + 64)`

= `sqrt(289)`

= 17 m

1. The area of the canvas used in making the tent

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

= πrl + 2πrH

= πr(l + 2H)

= `22/7 xx 15(17 + 2 xx 9)`

= `22/7 xx 15 xx 35`

= 1650 m²

2. Area of canvas bought for the tent

= (1650 + 30) m²

= 1680 m²

Now, this cost of the canvas height for the tent

= ₹ (1680 × 200)

= ₹ 3,36,000