Answer to Question #338063 in Mechanical Engineering for erix

Question

a cube with edge length of 10cm is inscribed in a sphere, what is the surface area of the sphere

Answer 1

The diameter $d$ of the sphere is

$$d=\sqrt{(10)^2+(10)^2+(10)^2}=10\sqrt{3} (cm)$$

The surface area $A$ of the sphere is

$$A=\pi d^2=\pi(10\sqrt{3})^2=300\pi({cm}^2)$$

The surface area of the sphere is $300\pi\ {cm}^2.$