Multiple choice

The radius of a cylinder is increased by 150% and its height is increased by 50%. What is the percentage increase in its volume?

  1. 375%

  2. 625.5%

  3. 775.75%

  4. 837.5%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume V = pi * r^2 * h. New radius R = 2.5r. New height H = 1.5h. New volume V' = pi * (2.5r)^2 * (1.5h) = pi * 6.25r^2 * 1.5h = 9.375 * pi * r^2 * h = 9.375V. The increase is 8.375V, which is 837.5%.

AI explanation

Let the original radius and height be r and h. A 150% increase makes the new radius 2.5r, and a 50% increase makes the new height 1.5h. Using the volume of a cylinder formula, the new volume is pi times 2.5r squared times 1.5h, which equals 9.375 times pi times r squared times h. The percentage increase is 9.375 minus 1 = 8.375, yielding an 837.5% increase.

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