Multiple choice

A cube is cut into 64 identical smaller cubes. On one face of each smaller cube, 25 identical circles of maximum radius are drawn in a square grid. The sum of the diameters of four circles is 20 units. Find one-fourth of the maximum volume of the largest cylinder that can fit inside the original cube.

  1. 7,000π

  2. 5,000π

  3. 62,500π

  4. 15,625π

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The problem is poorly defined. If 25 circles of max radius are in a square grid on a face, the side of the square is 10*diameter. The sum of 4 diameters is 20, so diameter = 5. Side of small cube = 25. Original cube side = 4 * 25 = 100. Largest cylinder in cube has diameter 100 and height 100. Volume = pi * r^2 * h = pi * 50^2 * 100 = 250,000 * pi. One-fourth of this is 62,500 * pi.

AI explanation

The original cube is divided into 64 identical smaller cubes, meaning there are 4 small cubes along each edge, so the side length of the original cube is 4 multiplied by 50 units to equal 200 units. The largest cylinder that fits inside this original cube has a radius of 100 units and a height of 200 units, making its maximum volume pi times 100 squared times 200, which equals 2,000,000 pi. Taking one-fourth of this maximum volume results in 500,000 pi.

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