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In Fig. 3, a tent is in the shape of a cylinder surmounted by a conical top of same diameter. If the height and diameter of cylindrical part are $2.1 m$ and $3 m$ respectively and the 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 $500 per sq . meter$ . $[Use π = \frac{22}{7}]$

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Rs 16500

Rs 16520

Rs 16300

Rs 16400

answer is A.

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Detailed Solution

Given that,
Question Image

Radius of the conical part = radius of cylindrical part r =

\frac{3}{2}

m.
Slant height of the cone l = 2.8 m.
Height of the cylinder, h = 2.1 m.
Surface area of cone =

πrl

Surface area of cylinder =

2 rπh

Now, The surface area of the tent = surface area of cone + surface area of cylinder

Area of canvas required = πrl + 2 rπh

\Rightarrow \frac{22}{7} \times \frac{3}{2} \times 2.8 + 2 \times \frac{22}{7} \times \frac{3}{2} \times 2.1

\Rightarrow \frac{33}{7} (2.8 + 4.2)

\Rightarrow \frac{33}{7} (7.0)

\Rightarrow 33

The total cost of canvas,

500 \times 33 = Rs . 16500 .

Thus, the total cost of canvas needed to make the tent is

Rs . 16500 .

Hence, option 1 is the correct answer.

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