Multiple choice

If a solid piece of iron is in the form of a cuboid of dimensions $49$ cm $\times33$ cm $\times 24$ cm is moulded to form a solid sphere, then the radius of the sphere is

  1. $21$ cm
  2. $23$ cm
  3. $25$ cm
  4. $19$ cm
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A Correct answer
Explanation

The volume of the cuboid is 49 * 33 * 24 = 38808 cm^3. The volume of a sphere is (4/3) * pi * r^3. Setting (4/3) * (22/7) * r^3 = 38808, we get r^3 = 38808 * 21 / 88 = 9261. The cube root of 9261 is 21.

AI explanation

When the cuboid is moulded into a sphere, the volumes remain equal, so 49 * 33 * 24 equals (4/3) * pi * radius^3. The product of the dimensions is 38808. Setting 38808 equal to (4/3) * pi * radius^3 and solving using pi as 22/7 gives radius^3 as 9261. The cube root of 9261 is 21 cm.

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