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

Answer 1

Let the length of the side of the cube be ${}^{\prime }{a}^{\prime }.$

$\therefore V_1$​ = (Volume of the cube) $=a^3$

Now, Length of side of cube = Diameter of the sphere $=a$

Hence, Radius of sphere $=\frac{a}{2}$

$V_2$ = (Volume of sphere) $=\frac{4}{3}\pi r^3=\frac{4}{3}\pi (\frac{a}{2}{)}^3=\frac{4}{3}\pi \times \frac{a^3}{8}$​

Ratio of $V_1$ and $V_2$ $=\frac{a^3}{\frac{4}{3}\pi \times \frac{a^3}{8}}=6:\pi$