Multiple choice

Calculate the approximate edge length of a cube having the same volume as a sphere of radius $5$cm.

  1. $5.00$
  2. $5.50$
  3. $6.24$
  4. $8.06$
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D Correct answer
Explanation

The volume of a sphere is (4/3) * pi * r^3. With r=5, volume = (4/3) * pi * 125 = 523.6. A cube with volume s^3 = 523.6 has an edge length s = cbrt(523.6) which is approximately 8.06.

AI explanation

The volume of the sphere is calculated using the formula four thirds times pi times radius cubed, which is four thirds times 3.14159 times 5 cubed, yielding approximately 523.6 cubic cm. For a cube to have this same volume, its edge length must be the cube root of 523.6. Taking the cube root gives an approximate edge length of 8.06 cm.

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