Answer:
 5.  512 cubic units
 6.  268.1 cubic units
 7.  243.9 cubic units
Step-by-step explanation:
5. The formula for the volume of a cube in terms of edge length s is ...
 V = s^3
This cube has an edge length of 8 units, so the volume is ...
 V = (8 units)^3 = 512 units^3 . . . . volume of cube
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6. The formula for the volume of a sphere in terms of radius is ...
 V = (4/3)πr^3
When the diameter is given, the radius is half the diameter, so we can write the formula as ...
 V = (4/3)π(d/2)^3 = (4/3)πd^3/8
 V = (π/6)d^3
When the sphere has the same diameter as the edge length of the cube, the volume is π/6 times that of the enclosing cube.
 V = (π/6)(512 units^3) ≈ 268.1 units^3 . . . . . sphere volume
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7. The difference in volumes is ...
 (512 -268.1) units^3 = 243.9 units^3 . . . . . remaining cube volume
