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27 April, 07:53

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?

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  1. 27 April, 08:22
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    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.
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