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A cube has a side length of 5.6 cm. What is the volume of the largest sphere that can be carved out from this cube?

1. 91.98 cm^3
2. 99.96 cm^3
3. 96.98 cm^3
4. 90.69 cm^3

Correct answer: 91.98 cm^3

Solution

The largest sphere that fits inside a cube of side 5.6 cm has radius r = 2.8 cm. V = (4/3)(22/7)(2.8)^3 = (4/3)(22/7)(21.952) = 91.97 cm^3, which rounds to 91.98 cm^3.

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