Multiple choice

If the radius of a right circular cone is increased by 50%, its volume increases by

  1. 75%

  2. 100%

  3. 125%

  4. 237.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cone is V = (1/3) * pi * r^2 * h. If the radius increases by 50%, the new radius is 1.5r. The new volume is (1/3) * pi * (1.5r)^2 * h = 2.25 * V. The increase is 2.25 - 1 = 1.25, or 125%.

AI explanation

The volume of a right circular cone is directly proportional to the square of its radius when the height remains constant. The formula for volume is (1/3)*pi*r^2*h, so increasing the radius by 50% changes the radius multiplier to 1.5. The new volume multiplier becomes (1.5)^2 = 2.25, which means the volume increases by 125%.

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