Question 24

As sphere is inscribed in a cube that has surface area of $$24\text{cm}^2$$. A second cube is then inscribed within the sphere. The surface area of the inner cube (in $$\text{cm}^2$$) is

Correct Answer: 8

Solution

The outer cube's side satisfies $$6s^2=24$$, so $$s=2$$, and the inscribed sphere has radius 1 and diameter 2. This diameter equals the inner cube's space diagonal, so if the inner cube has side $$a$$, $$a\sqrt{3}=2$$, giving $$a^2=\frac{4}{3}$$. Its surface area is $$6a^2=6\times\frac{4}{3}=8$$.

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As sphere is inscribed in a cube that has surface area of $$24\text{cm}^2$$. A second cube is then inscribed within the sphere. The surface area of the inner cube (in $$\text{cm}^2$$) is

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