Multiple choice

A solid consists of a circular cylinder fitted with right circular cone placed on the top. The height of the cone is 9 cm. If total volume of the solid is 3 times the volume of the cone, find the height of the circular cylinder.

  1. 6 cm

  2. 7 cm

  3. 8 cm

  4. 7.5 cm
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A Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * 9 = 3 * pi * r^2. Volume of solid = Volume of cylinder + Volume of cone = pi * r^2 * H + 3 * pi * r^2. Given Volume of solid = 3 * Volume of cone = 3 * (3 * pi * r^2) = 9 * pi * r^2. So, pi * r^2 * H + 3 * pi * r^2 = 9 * pi * r^2. H + 3 = 9, so H = 6 cm.

AI explanation

Let the height of the cylinder be H. The total volume is the sum of the cylinder volume and the cone volume, so pi * r^2 * H + (1/3) * pi * r^2 * 9 = 3 * [(1/3) * pi * r^2 * 9]. Simplifying this equation gives pi * r^2 * H + 3 * pi * r^2 = 9 * pi * r^2. Solving for H yields H = 6 cm. The result is 6 cm.

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