Multiple choice

A right circular cylinder of maximum volume is cut out from a solid wooden cube. The material left is what percent of the volume (nearest to an integer) of the original cube?

  1. 19

  2. 28

  3. 23

  4. 21
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cube side = s. Volume = s^3. Max cylinder has height s and radius s/2. Volume = pi * (s/2)^2 * s = pi * s^3 / 4. Volume = 3.14159 * s^3 / 4 = 0.7854 * s^3. Leftover = 1 - 0.7854 = 0.2146, which is 21%.

AI explanation

Let the side of the cube be s, making its original volume s^3. The maximum volume cylinder cut from it has a base radius of s/2 and a height of s, giving a cylinder volume of 22/7 * (s/2)^2 * s = 11s^3/14. The material left is s^3 - 11s^3/14 = 3s^3/14, which is (3/14) * 100 = 21.4 percent. Rounding to the nearest integer gives 21 percent.

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