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 are2.1m and3m respectively and the slant height of conical part is 2.8m 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=227]

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Q.

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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a

Rs 16500

b

Rs 16520

c

Rs 16300

d

Rs 16400

answer is A.

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Detailed Solution

Given that,
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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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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 are2.1m and3m respectively and the slant height of conical part is 2.8m 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=227]