5. What is the volume of the cube on the right? Round to the nearest tenth.
6. What is the volume of the sphere?
7. If the sphere was dugout of the cube what is the volume of the cube?

  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