Cube A is inscribed in sphere B, which is inscribed in cube C. If the sides of cube A have length 4, what is the volume of cube C?

The volume of cube C is

Step-by-step explanation:

step 1

Find the diameter of sphere B

we know that

When a cube is inscribed in a sphere, the long diagonal of the cube is a diameter of the sphere

Let

L ----> the length side of cube A

d ----> the diagonal of the base of cube A

D ---> the long diagonal of cube A

Find the diagonal of the base of cube A

Applying the Pythagorean Theorem

we have

substitute

Find the long diagonal of cube A

Applying the Pythagorean Theorem

substitute

step 2

we know that

If sphere B is inscribed in cube C, then the length side of cube C is equal to the diameter of sphere B

Let

c ----> the length side of cube C

we have that

The volume of cube C is equal to

substitute

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

126.66 m²

step-by-step explanation:

the pertinent area formula is a = πr², where r is the radius.

here, a = π(6.35 m)² = 40.32π, or approximately 126.66 m²