To find the volume of air inside the cube, we first need to find the volume of the cube itself and then subtract the volume of the ball from it.
The volume of a cube is given by the formula: \( \text{Volume}_{\text{cube}} = \text{side}^3 \).
Given that each side of the cube measures 9.5 inches, we can plug this into the formula:
\( \text{Volume}_{\text{cube}} = 9.5^3 \)
\( \text{Volume}_{\text{cube}} = 857.375 \) cubic inches (approximately)
Now, to find the volume of air inside the cube, we subtract the volume of the ball (268 cubic inches) from the volume of the cube:
\( \text{Volume}_{\text{air}} = \text{Volume}_{\text{cube}} - \text{Volume}_{\text{ball}} \)
\( \text{Volume}_{\text{air}} = 857.375 - 268 \)
\( \text{Volume}_{\text{air}} = 589.375 \) cubic inches
Rounding to the nearest tenth, the volume of air inside the cube is approximately 589.4 cubic inches. So the correct answer is: 589.4 cubic inches.
