The small ball inside the cubed display case has a volume of 8 cubic inches. If the free space inside the display case is 216 cubic inches, then how tall is the display case?

the display case is 6.07 in tall.

Step-by-step explanation:

Step 1:

The volume of the empty is determined by taking the difference between the volume of the ball and the volume of the cube. Therefore,

V_empty = V_cube - V_ball

V_cube = V_empty + V_ball

V_cube = 216 in³ + 8 in³

V_cube = 224 in³

Thus, the volume of the cubed display is 224 in³.

Step 2:

The volume of a cube is:

V_cube = l³

Thus,

l = ∛[V_cube]

l = ∛[224 in³]

l = 6.07 in

Therefore, the display case is 6.07 in tall.