Multiple choice

In a research facility, a cylindrical tank containing water has a total volume of 864π cubic meters. The researchers plan to transfer this water into four conical flasks. Each conical flask has the same radius as that of the cylindrical tank. However, the height of each conical flask is three times the radius of the conical flask. What is the height, in meters, of each conical flask?

  1. 6

  2. 12

  3. 18

  4. 24
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C Correct answer
Explanation

The volume of the cylinder is 864pi. The volume of one cone is (1/3) * pi * r^2 * h. Since h = 3r, the volume of one cone is (1/3) * pi * r^2 * (3r) = pi * r^3. Four such cones have a total volume of 4 * pi * r^3. Equating 4 * pi * r^3 = 864pi, we get r^3 = 216, so r = 6. Since h = 3r, h = 3 * 6 = 18.

AI explanation

The total volume of the cylindrical tank is 864 pi, and since this is divided equally into four conical flasks, the volume of each flask is 216 pi. Using the cone volume formula of 1/3 times pi times radius squared times height, and substituting the given relationship that height equals three times the radius, we get 216 pi equals 1/3 times pi times radius squared times 3 times radius. This simplifies to 216 pi equals pi times radius cubed, making the radius 6 meters. Because the height is three times the radius, the height of each flask is 18 meters.

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