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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.

Q : 8    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 Rs 12 per \small m^2, what will be the cost of painting all these cones? (Use \small \pi =3.14 and take \small \sqrt{1.04}=1.02)
 

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Given, hollow cone.

The base diameter of the cone = d = 40\ cm = 0.4\ m

Height of the cone = h = 1\ m

\therefore Slant height = l = \sqrt{h^2+r^2}= \sqrt{1^2+0.2^2}

We know, Curved surface area of a cone =\pi r l = \pi r\sqrt{h^2+r^2}

\therefore The curved surface area of 1 cone = 3.14\times0.2\times\sqrt{1.04} = 3.14\times0.2\times1.02

= 0.64056\ m^2

\therefore The curved surface area of 50 cones= (50\times0.64056)\ m^2

= 32.028\ m^2

Now, the cost of painting \small 1\ m^2 area = \small Rs.\ 12

\therefore  Cost of the painting 32.028\ m^2 area = Rs.\ (32.028\times12)

= Rs.\ 384.336

Therefore, the cost of painting 50 such hollow cones is Rs.\ 384.34\ (approx)

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