Answer:
347.3 cubic units
Step-by-step explanation:
To calculate the volume of the empty space, we derive the total volume of the two shapes and subtract the volume of the sphere from that of the cube.
The volume of a cube is calculated as l^3.
Here, the length is given as 9, so we compute 9x9x9, resulting in 729 cubic units.
The formula for the volume of a sphere is 4/3 pi r^3.
The radius is 4.5 (half of the diameter), thus:
4/3*91.125 pi
which becomes 121.5 pi = 381.7 (to one decimal place).
Subtracting these gives us 729-381.7 = 347.3.
The volume of the empty space equals 347.3 cubic units.
The comprehensive expression in reference to the given d:
Volume of empty space = d^3 - 4/3 pi (d/2)^3
I hope this was helpful!
