Mensuration Practice Test 8

When a sphere is inscribed in a cube, then edge of a cube is equal to the diameter of a sphere.
So, Diameter = 6 cm
Diagonal of cube = $\sqrt{3{\mathit{a}}^2}$
= $\sqrt{3{\mathit{a}}^2}$
= $\sqrt{3\times 36}$
= $\sqrt{108}$
= $6\sqrt{3}$ cm
Distance from the vertex = $\frac{\mathrm{Diagonal}-\mathrm{Diameter}}{2}$
= $\frac{6\sqrt{3}-6}{2}$
= $3\left(\sqrt{3}-1\right)$ cm