Answer:
347.3 cubic units
Step-by-step explanation:
To find the area of empty space, we can find the volume of both shapes and subtract the volume of the sphere from the volume of the cube.
Volume of a cube = l^3
Our given length in this case is 9, so the volume is 9x9x9= 729 cubic units.
The volume of sphere = 4/3 pi r^3
Our radius is 4.5 (half of diameter), so:
4/3*91.125 pi
121.5 pi = 381.7 (1dp)
729-381.7 = 347.3
The volume of empty space = 347.3 cubic units.
The full expression in terms of given d:
Volume of empty space = d^3 - 4/3 pi (d/2)^3
Hope this helped!
