Question

A sphere has a radius of 4 inches. What is the surface area of the smallest cube that could circumscribe the sphere?

Answer 1

Answer:

$SA=384\ in^2$

Step-by-step explanation:

we know that

The smallest cube that could circumscribe the sphere has a length side equal to the diameter of the sphere

In this problem

The radius of the sphere is $r=4\ in$

The diameter of the sphere is two times the radius

$D=2r=2(4)=8\ in$

so

The length side of the cube is

$b=8\ in$

Remember that

The surface area of a cube is equal to the area of its six faces

so

$SA=6b^2$

substitute the value of b

$SA=6(8)^2$

$SA=384\ in^2$