Sphere circumscribed about a cube

Text

A cube has edge $8$ cm. Find the radius and the surface area of the sphere circumscribed about the cube.

Solution

The diameter of the circumscribed sphere is the cube’s diagonal: $d=8\sqrt3$, so $R=4\sqrt3\approx6.93$ cm. Surface: $S=4\pi R^2=4\pi\cdot48=192\pi\approx603.19$ cm$^2$. $\boxed{R=4\sqrt3\approx6.93\ \text{cm};\ S=192\pi\approx603.19\ \text{cm}^2}$