Question

A tent of height 3.3 m is in the form of a right circular cylinder of diameter 12m and height 2.2m, surmounted by a right circular cone of the same diameter. Find the cost of the canvas of the tent at the rate of Rs. 500 per m2.

Answer 1

Given:

The height of the tent = 3.3 m

The diameter of the base of the cylinder or cone, d = 12 m

The height of the cylindrical part of the tent, h = 2.2 m

To find:

The cost of the canvas of the tent at the rate of Rs. 500 per m²

Solution:

Step 1:

The radius of the base of the tent, r = $\frac{12}{2}$ = 6 m

and

The height of the conical part of the tent is given by,

= [Height of the tent] - [Height of the cylindrical part of the tent]

= 3.3 - 2.2

= 1.1 m

To find the slant height of the cone we have the formula as,

Slant Height, $\boxed{l \:=\:\sqrt{h^2\:+\:r^2} }$

here, h = height of the cone and r = radius of the cone

∴ l = $\sqrt{1.1^2\:+\:6^2} = \sqrt{1.21\:+\:36} = \sqrt{37.21} = 6.1 \:m$

Therefore,  

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 * $\frac{22}{7}$ * 6 * 2.2] + [$\frac{22}{7}$ * 6 * 6.1]

= [82.971 m²] + [115.028 m²]

= 197.99 m²

≈ 198 m²

Step 2:

Now,

The cost of the canvas is given as Rs. 500 per metre square.

Thus,

The cost of making the tent with the required area of canvas i.e., 198 m² is,

= 198 m² * Rs. 500

= Rs. 99000

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Also View:

A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and the slant height of the conical portion is 53 m, find the area of canvas needed to make the tent.

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A circus tent is cylindrical to a height of 15 m and conical above it. If its base radius is28 m and the slant height of the conical portion is 35 m, find the area of canvas needed to make the tent and the volume of air inside the tent

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Answer 2

Answer:

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