Multiple choice

Two cylindrical tanks are placed side by side on a level surface. The first tank has a radius of 4 metres, a height of 10 metres and is full of water. The second tank has a radius of 6 metres, a height of 8 metres and is empty. Water is pumped from the first tank into the second until the depth of water in both the tanks is the same. The depth of water in each tank is approximately _________.

  1. 6.07 m

  2. 5.07 m

  3. 4.07 m

  4. 3.07 m

  5. 2.07 m
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D Correct answer
Explanation

Total volume of water = pi * 4^2 * 10 = 160*pi. Total base area = pi * 4^2 + pi * 6^2 = 16*pi + 36*pi = 52*pi. Depth = Total Volume / Total Base Area = 160*pi / 52*pi = 160/52 = 40/13 = 3.0769... m.

AI explanation

The volume of water transferred from the first tank equals the volume accumulated in the second tank, which establishes the equation pi times 4 squared times the height difference equals pi times 6 squared times the final water depth. If the equal final depth in both tanks is h, the first tank loses 10 minus h metres of water while the second tank gains h metres of water. This gives the equation 16 times 10 minus h equals 36 h. Solving for h yields 160 equals 52 h, making the depth approximately 3.07 metres.

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