The expression volume of empty space in the cube is [tex]\rm (9)3 -\dfrac{4}{3}\pi (4.5)^3[/tex].
Given
A sphere with a diameter of 9 units fits exactly in the clear glass cube as shown.
What is the formula of volume of a sphere?
The formula of the volume of a sphere is;
[tex]\rm Volume = \dfrac{4}{3}\pi r^3[/tex]
Where r is the radius of the sphere.
The radius of the sphere is;
[tex]\rm Radius = \dfrac{Diameter}{2}\\\\Radius= \dfrac{9}{2}\\\\Radius = 4.5[/tex]
Then,
The volume of the sphere is;
[tex]\rm Volume = \dfrac{4}{3}\pi r^3\\\\\rm Volume = \dfrac{4}{3}\times \pi \times (4.5)^3\\[/tex]
And the volume of the cube is;
[tex]\rm Volume = a^3\\\\Volume = (9)^3[/tex]
Therefore,
The expression volume of empty space in the cube is;
The volume of empty space = [tex]\rm (9)3 -\dfrac{4}{3}\pi (4.5)^3[/tex]
Hence, the expression volume of empty space in the cube is [tex]\rm (9)3 -\dfrac{4}{3}\pi (4.5)^3[/tex].
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