Multiple choice

A cylindrical tank has a height that is twice its radius. If the height of the tank is increased by 50% while the radius remains unchanged, by what percentage will the volume of the tank increase?

  1. 40%

  2. 50%

  3. 75%

  4. 100%

  5. 150%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial volume V = pi * r^2 * h = pi * r^2 * (2r) = 2 * pi * r^3. New height h' = 1.5 * h = 3r. New volume V' = pi * r^2 * (3r) = 3 * pi * r^3. Increase = (3 - 2) / 2 = 50%.

AI explanation

Let the initial radius be r, making the initial height 2r and the initial volume pi*r^2*2r = 2*pi*r^3. The new height is increased by 50%, making it 3r, so the new volume is pi*r^2*3r = 3*pi*r^3. The increase in volume is 3*pi*r^3 - 2*pi*r^3 = pi*r^3. The percentage increase is calculated as (pi*r^3 / 2*pi*r^3) * 100, which equals 50%.

Keep practicing — related questions