Multiple choice

The cube has volume $64$ cubic units. If a largest sphere possible that can be placed inside this cube has radius $r$, then the value of $r$ is

  1. $2$
  2. $\displaystyle 2\sqrt { 2 } $
  3. $4$
  4. $8$
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A Correct answer
Explanation

The volume of a cube is s^3 = 64, so the side length s is 4. The diameter of the largest sphere that fits inside a cube is equal to the side length of the cube, so 2r = 4, which means r = 2.

AI explanation

The volume of a cube is found by cubing its side length, so the side of this cube is the cube root of 64, which is 4 units. The largest sphere that can fit inside this cube must have a diameter equal to the side length of the cube. Therefore, the radius r is half of 4, making it 2.

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