Multiple choice

A right circular cone has base radius 5 cm. If the radius is increased by 20% without any change in height of the cone, then the percentage increase in volume is

  1. 44%

  2. 40%

  3. 25%

  4. 22%
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A Correct answer
Explanation

Volume V = (1/3) * pi * r^2 * h. If r increases by 20%, the new radius is 1.2r. New volume V' = (1/3) * pi * (1.2r)^2 * h = 1.44 * V. The increase is 44%.

AI explanation

The volume of a right circular cone is proportional to the square of its base radius when the height is constant, as seen in the formula V = (1/3) * pi * r^2 * h. An increase of 20% in the radius makes the new radius 1.2 times the original, so the new volume becomes proportional to 1.2^2, or 1.44. This means the new volume is 144% of the original volume, representing an increase of 44%.

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