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Answer:
Step-by-step explanation:
volume of box - volume of sphere = unused space
L X W X H - 4/3 pi r^3
17. 8 x 17.8 x 17.8 - 4/3 ( 3.14) ( 17.8/2)^3 = 2688.28 units^3
Answer:
Volume not taken up by the globe is 2688.28 units^3.
Step-by-step explanation:
To solve this problem, we require two formulas: the volume of a sphere and the volume of a cube. They are..
[tex]V_{c} = a^3 \\V_{s} = \frac{4}{3} \pi r^3[/tex]
Our given values are:
globe diameter of 17.8 units
cube side length of 17.8 units
To, get the volume of the sphere, we need the radius which can be obtained by dividing the diameter by 2.
17.8/2 = 8.9
radius of globe = 8.9 units
Now we can solve for the volumes of both objects.
[tex]V_{c} = a^3 \\V_{c} = 17.8^3 \\V_{c} = 5639.752 units^3[/tex]
[tex]V_{s} = \frac{4}{3} \pi (r^3)\\V_{s} = \frac{4}{3} \pi (8.9^3)\\V_{s} = \frac{4}{3} \pi (r^3) \\V_{s} = 2951.470213 units^3[/tex]
[tex]V_{nt} = 5639.752 - 2951.470213 \\V_{nt} = 2688.281787 \\[/tex]
Round to nearest hundredth.
V = 2688.28