Multiple choice

The volume of right cylinder $14 cm$ in height is equal to that of a cube whose edge is $11 cm$. The radius of the base of the cylinder is

  1. $5.2 cm$
  2. $5.5 cm$
  3. $11 cm$
  4. $22 cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cube = 11^3 = 1331 cm^3. Volume of cylinder = pi * r^2 * h = (22/7) * r^2 * 14 = 44 * r^2. Setting 44 * r^2 = 1331, r^2 = 1331 / 44 = 30.25. r = sqrt(30.25) = 5.5 cm.

AI explanation

Equate the volume of the right cylinder to the volume of the given cube to find the cylinder's base radius. The cube's volume is its edge cubed, giving 11 times 11 times 11, which equals 1331 cubic cm. The cylinder's volume is pi times radius squared times height, so we have twenty-two sevenths times radius squared times 14 equals 1331. Simplifying the left side gives 44 times radius squared equals 1331, and solving for the radius squared gives 30.25. Taking the square root of 30.25 results in a radius of 5.5 cm.

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