Multiple choice

If a cylinder of radius 4 cm and height 8 cm is melted and constructed into a cone of the same radius, then what will be the height of this cone?

  1. 48 cm

  2. 24 cm

  3. 8 cm

  4. 12 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 4^2 * 8 = 128 * pi. Volume of cone = (1/3) * pi * r^2 * H = (1/3) * pi * 4^2 * H = (16/3) * pi * H. Equating volumes: 128 * pi = (16/3) * pi * H. H = 128 * 3 / 16 = 8 * 3 = 24 cm.

AI explanation

Because the volumes remain equal when the cylinder is melted and recast into a cone, use the formula pi * r^2 * h equals (1/3) * pi * r^2 * H, where H is the height of the new cone. Substituting the given values gives pi * 4^2 * 8 equals (1/3) * pi * 4^2 * H. Simplifying this equation by canceling pi and 4^2 from both sides leaves 8 equals H / 3. Solving for H gives a height of 24 cm.

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