Multiple choice

A cone with radius 7 m has volume 1232 m3. What is the cost of painting the curved surface of the cone at the rate of Rs. 20 per m2?

  1. Rs. 7500

  2. Rs. 9000

  3. Rs. 10,500

  4. Rs. 11,000

  5. Rs. 12,700
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume V = (1/3) * pi * r^2 * h. 1232 = (1/3) * (22/7) * 7^2 * h => 1232 = (1/3) * 22 * 7 * h => h = 24. Slant height l = sqrt(r^2 + h^2) = sqrt(7^2 + 24^2) = 25. Curved surface area = pi * r * l = (22/7) * 7 * 25 = 550. Cost = 550 * 20 = 11000.

AI explanation

Using the cone volume formula V = (1/3) * pi * r^2 * h, we get 1232 = (1/3) * (22/7) * 7^2 * h, which gives h = 24 m. The slant height is found using l = sqrt(r^2 + h^2) = sqrt(7^2 + 24^2) = 25 m. The curved surface area is pi * r * l = (22/7) * 7 * 25 = 550 m^2. Multiplying this by the rate gives the total cost of 550 * 20 = Rs. 11,000.

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