Answer:
[tex]SA=384\ in^2[/tex]
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 [tex]r=4\ in[/tex]
The diameter of the sphere is two times the radius
[tex]D=2r=2(4)=8\ in[/tex]
so
The length side of the cube is
[tex]b=8\ in[/tex]
Remember that
The surface area of a cube is equal to the area of its six faces
so
[tex]SA=6b^2[/tex]
substitute the value of b
[tex]SA=6(8)^2[/tex]
[tex]SA=384\ in^2[/tex]
