Multiple choice

A solid vessel of cylindrical shape, having volume of 33.264 litres, is cast into a conical shape of height 72 cm. What is the cost of painting its CSA at Rs. 12 per sq. m?

  1. Rs. 5.94

  2. Rs. 6.94

  3. Rs. 7.95

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cylinder = 33.264 liters = 0.033264 m^3. Converted to cm^3, it is 33264 cm^3. Using V = (1/3) * pi * r^2 * h, we find r = 21 cm. The slant height l = sqrt(r^2 + h^2) = sqrt(21^2 + 72^2) = 75 cm. CSA = pi * r * l = (22/7) * 21 * 75 = 4950 cm^2 = 0.495 m^2. Cost = 0.495 * 12 = 5.94.

AI explanation

The volume of the cone equals the vessel's volume, which is 33264 cubic centimeters. Using the cone volume formula, V = (1/3) * pi * r^2 * h, we get 33264 = (1/3) * (22/7) * r^2 * 72, so r equals 7 centimeters. The slant height is found using l = sqrt(r^2 + h^2) = sqrt(7^2 + 72^2) = 72.34 centimeters. The curved surface area is pi * r * l = (22/7) * 7 * 72.34 = 4950 square centimeters, or 0.495 square meters. Multiplying by the rate of Rs. 12 gives a cost of Rs. 5.94.

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