Multiple choice

A metallic pipe of diameter 7 cm and length 10 cm is melted and recast into cones each of radius 3 cm and height 3 cm. Find the approximate number of cones thus formed.

  1. 15

  2. 10

  3. 13

  4. 12
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C Correct answer
Explanation

Volume of pipe = pi * r^2 * h = pi * (3.5)^2 * 10 = 122.5 * pi. Volume of cone = (1/3) * pi * 3^2 * 3 = 9 * pi. Number of cones = 122.5 / 9 = 13.61. Approximately 13.

AI explanation

The volumes must be equal when the pipe is recast, so we divide the cylindrical volume by the conical volume. The cylindrical volume is pi times the radius 3.5 squared times the height 10, which equals 385 cubic centimeters. Using the cone volume formula of one third pi times radius squared times height, each cone has a volume of 9 pi, or 28.28 cubic centimeters. Dividing 385 by 28.28 gives approximately 13.6, so the approximate number of cones formed is 13.

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