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A bus stop is barricaded from the remaining part of the road, by using 50 hollow cones made of recycled cardboard. Each cone has a base diameter of 40 cm and height 1 m. if the outer side of each of the cones is to be painted and the cost of painting is ₹12 per $m^{2}$ , what will be the cost of painting all these cones?

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Rs.

354.84

Rs . 394.84

Rs.

384.34

None of these

answer is C.

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Detailed Solution

Given :

h = 1 m; radius = \frac{40}{2} = 20 cm = 0.2 m

Slant height(

l

) is,

l^{2} = h^{2} + r^{2}

\Rightarrow

l^{2} = 1^{2} + {0.2}^{2}

\Rightarrow l = \sqrt{1 + 0.04} = \sqrt{1.04} = 1.02 m

Curved surface area of a cone

= πrl = (3.14 \times 0.2 \times 1.02) m^{2} = 0.64046 m^{2}

Curved surface area of 50 cones

= 50 \times 0.64046 = 32.028 m^{2}

Cost of painting

= (12 \times 32.028) = Rs . 384.34

Hence, the cost of painting is Rs.

384.34

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