Question
The volume of the largest possible cube that can be inscribed in a hollow spherical ball of radius r cm is :
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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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 :
$$\eqalign{
& = {a^3} \cr
& = {\left( {\frac{2}{{\sqrt 3 }}r} \right)^3} \cr
& = \frac{8}{{3\sqrt 3 }}{r^3} \cr} $$
Was this answer helpful ?
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