Multiple choice

A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. The radius of the cone will be

  1. 6 cm

  2. 8 cm

  3. 4 cm

  4. 5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the cylinder is pi * r^2 * h = pi * 8^2 * 2 = 128 * pi. The volume of the cone is (1/3) * pi * R^2 * H = (1/3) * pi * R^2 * 6 = 2 * pi * R^2. Equating the volumes, 2 * pi * R^2 = 128 * pi, so R^2 = 64, which means R = 8 cm.

AI explanation

Because the cylinder is melted to form the cone, their volumes must be equal according to the principle of conservation of volume. Setting the cylinder volume formula pi*8*8*2 equal to the cone volume formula (1/3)*pi*r^2*6 yields pi*128 = 2*pi*r^2. Solving for r^2 gives 64, so the radius of the cone is 8 cm.

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