Answer to Question #338535 in Geometry for hehehe

Question

a cube with edge length of 10 cm is inscribed in a sphere, what is the diameter of the sphere?

Answer 1

The cube's face is a square. The edge of cube is $10$ cm. Thus, the length of the side of the square is $10$ cm. The diagonal of the square is equal to $10\sqrt{2}$ due to the Pythagorean theorem. The diagonal of the cube is: $\sqrt{10^2+2\cdot10^2}=10\sqrt{3}$. It is equal to the diameter of the sphere.

Answer: $10\sqrt{3}$ cm.