Answer:
250/3π cubic inches
Step-by-step explanation:
we know that
The volume of the space between the cylinder and the sphere is equal to the volume of the cylinder minus the volume of the sphere
step 1
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=10\ in[/tex]
[tex]r=5\ in[/tex]
substitute
[tex]V=\pi (5)^{2} (10)[/tex]
[tex]V=250\pi\ in^{3}[/tex]
step 2
Find the volume of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=5\ in[/tex]
substitute
[tex]V=\frac{4}{3}\pi (5)^{3}[/tex]
[tex]V=(500/3)\pi\ in^{3}[/tex]
step 3
Find the difference
[tex]250\pi\ in^{3}-(500/3)\pi\ in^{3}=(250/3)\pi\ in^{3}[/tex]
