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The ratio of the volume of a cube to that of a sphere which will fit inside the cube is :
Answer & Solution
Correct Answer:
Option
C
Let the edge of the cube be a
Then, volume of the cube = a3
Radius of the sphere $$ = \left( {\frac{a}{2}} \right)$$
Volume of the sphere :
$$\eqalign{ & = \frac{4}{3}\pi {\left( {\frac{a}{2}} \right)^3} \cr & = \frac{{\pi {a^3}}}{6} \cr} $$
∴ Required ratio :
$$\eqalign{ & = {a^3}:\frac{{\pi {a^3}}}{6} \cr & = 6:\pi \cr} $$
Then, volume of the cube = a3
Radius of the sphere $$ = \left( {\frac{a}{2}} \right)$$
Volume of the sphere :
$$\eqalign{ & = \frac{4}{3}\pi {\left( {\frac{a}{2}} \right)^3} \cr & = \frac{{\pi {a^3}}}{6} \cr} $$
∴ Required ratio :
$$\eqalign{ & = {a^3}:\frac{{\pi {a^3}}}{6} \cr & = 6:\pi \cr} $$
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