A tent is in the form of a cylinder of diameter 4.2 m and height 4 m, is surmounted by a cone of equal base and height 2.8 m. Find the cost of canvas required for making the tent at ₹100 per sq.m.

₹ 6590

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₹ 7590

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₹ 8590

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₹ 9876

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Solution

The correct option is B
₹ 7590

The total surface area of the tent:

$T = 2 π r h_{1} + π r l π = \frac{22}{7}; r = 2.1 m h_{1} = height of the cylinder = 4 m h_{2} = height of the cone = 2.8 m l = slant height of the cone l = \sqrt{{2.8}^{2} + {2.1}^{2}} = 3.5 m$

So,

$T = (2 \times \frac{22}{7} \times 2.1 \times 4 + \frac{22}{7} \times 2.1 \times 3.5) T = 75.9 m^{2}$

Therefore, the total cost of canvas at ₹100 per sq meter = $75.9 \times 100 = ₹ 7590$ .

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