Question

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be$6:\pi$.

• A. $12:\pi$.
• B. $9:\pi$.
• C. $6:\pi$.
• D. $12:\pi$.

Answer 1

The correct option is C

$6:\pi$.

Volume of the cube $\left(V_1\right)=(Side{)}^3$

Radius of the sphere (r) $=\frac{Side}{2}$

Volume of sphere $\left(V_1\right)=\frac{4}{3}\pi \left(r^3\right)$

$=\frac{4}{3}\pi {\left(\frac{Side}{2}\right)}^3=\frac{4}{3}\pi \times {\left(\frac{Side}{8}\right)}^3$

$\therefore \frac{V_1}{V_2}=\frac{(side{)}^3}{\frac{4}{3}\pi \frac{(side{)}^3}{8}}=\frac{6}{\pi }$ or $6:\pi$