The volume of a shape is the amount of space in it.
The volume outside the cylinder, but inside the cube is 214.6 cubic inches
The given parameter is:
[tex]l = 10[/tex] ---- length of the cube
So, the volume of the cube is:
[tex]V_1 = l^3[/tex]
[tex]V_1 = 10^3[/tex]
[tex]V_1 = 1000[/tex]
The volume of the cylinder is:
[tex]V_2 = \pi r^2h[/tex]
The diameter (d) of the cylinder equals the length of the cube.
This means that:
[tex]d = l[/tex]
[tex]d = 10[/tex]
Divide by 2 to calculate the radius of the cylinder
[tex]r = \frac{10}{2}[/tex]
[tex]r = 5[/tex]
Also, the height of the cube is::
[tex]h =l[/tex]
[tex]h =10[/tex]
So, we have:
[tex]V_2 = \pi r^2h[/tex]
[tex]V_2 = \pi \times 5^2 \times 10[/tex]
[tex]V_2 = \pi \times 25 \times 10[/tex]
[tex]V_2 = \pi \times 250[/tex]
[tex]V_2 = 785.4[/tex]
So, the volume (V) outside the cylinder is:
[tex]V = V_1 - V_2[/tex]
[tex]V = 1000 - 785.4[/tex]
[tex]V = 214.6[/tex]
Hence, the volume outside the cylinder is 214.6 cubic inches
Read more about volumes at:
https://brainly.com/question/15861918
