Multiple choice

Choose the correct answer from the alternatives given. The radius of a metallic cylinder is 3 cm and its height is 5 cm. It is melted and moulded into small cones, each of height 1 cm and base radius 1 mm. The number of such cones formed, is

  1. 450

  2. 1,350

  3. 8,500

  4. 13,500
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of the cylinder is pi * R^2 * H = pi * 3^2 * 5 = 45 * pi cubic centimeters. Since 1 mm equals 0.1 cm, the volume of each cone is (1/3) * pi * r^2 * h = (1/3) * pi * 0.1^2 * 1 = pi / 300 cubic centimeters. Dividing the cylinder's volume by the cone's volume gives 45 * pi / (pi / 300) = 13,500 cones.

AI explanation

The volume of the metallic cylinder is V = πr^2h = π * 3^2 * 5 = 45π cm^3. The dimensions of each small cone are a height of 1 cm and a base radius of 1 mm, which is 0.1 cm, giving a cone volume of (1/3)π(0.1)^2(1) = 0.003333π cm^3. The number of cones is the cylinder volume divided by the cone volume, which is 45π / (1/300)π = 45 * 300 = 13,500.

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