What is the area of a sphere described about a cube with an edge of 3 cm?

Since the sphere is described about a cube, then all the vertices of the cube lie on the surface of the sphere, the center of the sphere is the intersection point of the diagonals of the cube, and the diameter of the sphere is equal to the length of the diagonal of the cube.

We draw a diagonal AC at the base of the cube, then, by the Pythagorean theorem, AC ^ 2 = AD ^ 2 + SD ^ 2 = 9 + 9 = 18.

In a right-angled triangle ABC, AB ^ 2 = AC ^ 2 + BC ^ 2 = 18 + 9 = 27.

AB = D = 3 * √3 cm.

Let’s define the area of the sphere.

Ssph = n * D ^ 2 = n * (3 * √3) ^ 2 = 27 * n cm2.

Answer: The area of the sphere is 27 * n cm2.