Multiple choice

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are translated into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, then how much beverage is contained in the vessel from the bowl?

  1. $66 \frac {2}{3}$%
  2. $78 \frac {1}{2}$%

  3. 100%

  4. More than 100 % (i.e., some liquid will be the left in the bowl)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Bowl volume = (2/3)pi*r^3. Cylinder: radius R = 1.5H. Diameter is same, so 2R = 2r, so R = r. Thus H = r/1.5 = 2r/3. Cylinder volume = pi*R^2*H = pi*r^2*(2r/3) = (2/3)pi*r^3. The volumes are equal, so 100% of the beverage fits.

AI explanation

The volume of the hemispherical bowl is two thirds times pi times r cubed, and since the diameter is the same, this is the total beverage available. The radius of the cylinder is 50 percent more than its height, meaning the cylinder height is two thirds of r, making its volume pi times r squared times two thirds r, which also equals two thirds times pi times r cubed. Because the volumes match, the vessel contains exactly 100 percent of the beverage.

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