The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is :
Options:
A . $$\frac{2}{{\sqrt 3 }}{r^2}$$
B . $$\frac{4}{{\ 3 }}{r^2}$$
C . $$\frac{8}{{3\sqrt 3 }}{r^3}$$
D . $$\frac{1}{{3\sqrt 3 }}{r^3}$$
Answer: Option C Clearly, the diagonal of the largest possible cube will be equal to the diameter of the sphere Let the edge of the cube be a $$\eqalign{ & \sqrt 3 a = 2r \cr & \Rightarrow a = \frac{2}{{\sqrt 3 }}r \cr} $$ Volume : $$\eqalign{ & = {a^3} \cr & = {\left( {\frac{2}{{\sqrt 3 }}r} \right)^3} \cr & = \frac{8}{{3\sqrt 3 }}{r^3} \cr} $$
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