Question

4. The surface area of a cube is 486 in. Find the volume inside the cube but outside of

an inscribed sphere. Round to the nearest tenth.

Answer 1

Let s be the length of a side of the cube, then its surface area is given by 6s^2. We know that the surface area of the cube is 486 in^2, so we can set up the equation:

6s^2 = 486

Solving for s, we get:

s^2 = 81

s = 9

Therefore, the length of a side of the cube is 9 in. The radius of the inscribed sphere is half the length of a side, so it is r = 4.5 in. The volume inside the cube but outside of the sphere is equal to the volume of the cube minus the volume of the sphere:

V = s^3 - (4/3)πr^3

V = 9^3 - (4/3)π(4.5)^3

V ≈ 328.8 in^3

Rounding to the nearest tenth, the volume inside the cube but outside of the inscribed sphere is approximately 328.8 in^3.