Multiple choice

If a cylindrical vessel of 50 m diameter and height of 36 m holds liquid chemical 120 times a hemispherical bowl holds, find the radius of the hemispherical bowl.

  1. 6.55 m

  2. 13.10 m

  3. 19.65 m

  4. 25.55 m

  5. None of these
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A Correct answer
Explanation

Cylinder volume = pi * r^2 * h = pi * 25^2 * 36 = 22500 * pi. Hemispherical bowl volume = (2/3) * pi * R^3. 120 * (2/3) * pi * R^3 = 22500 * pi. 80 * R^3 = 22500. R^3 = 281.25. R = cube root of 281.25 approx 6.55.

AI explanation

The volume of the cylinder equals the volume of 120 hemispherical bowls, so pi times 25 squared times 36 equals 120 times two-thirds times pi times r cubed. This simplifies to 22500 equals 80 times r cubed. Solving for r gives a value of approximately 6.55 m.

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