Multiple choice

If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?

  1. 54 cm

  2. 9 cm

  3. 27 cm

  4. 13.5 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 7^2 * 9 = 441 * pi. Volume of cone = (1/3) * pi * r^2 * h_cone. Since radii are equal, 441 * pi = (1/3) * pi * 49 * h_cone. 441 = (49/3) * h_cone. h_cone = 441 * 3 / 49 = 9 * 3 = 27 cm.

AI explanation

Let h be the new height of the cone. Because the cylinder and cone have the same radius and volume, the cylinder volume formula, pi times 7 squared times 9, equals the cone volume formula, one third times pi times 7 squared times h. Solving for h, we multiply 9 by 3 to get 27 cm.

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