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Question 50
The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is
Solution
For the largest possible cube (of side a) in a sphere with radius r:
Diagonal of cube = diameter of the sphere, which is $$a\sqrt{\ 3}$$= 2r, or a = $$\ \frac{\ 2r}{\sqrt{\ 3}}$$
Now, the volume of this cube is $$a^3$$, or $$\ \frac{\ 8r}{3\sqrt{\ 3}}\ cm^3$$
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