Answer:
Part a) The equation for the volume of the film canister is
[tex]32\pi=\pi r^{2}(8)[/tex]
Part b) The radius of the film canister is [tex]2\ cm[/tex]
Step-by-step explanation:
The complete question is
A film canister in the shape of a cylinder has a height of 8 centimeters and a volume of 32π cubic centimeters.
a. Write an equation for the volume of the film canister.
b. What is the radius of the film canister?
Part a) Write an equation for the volume of the film canister
we know that
The volume of a cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
where
r is the radius of the circular base
h is the height of the cylinder
we have
[tex]V=32\pi\ cm^3[/tex]
[tex]h=8\ cm[/tex]
substitute
[tex]32\pi=\pi r^{2}(8)[/tex] ----> equation for the volume of the film canister
Part b) What is the radius of the film canister?
we have
[tex]32\pi=\pi r^{2}(8)[/tex]
[tex]32\pi=8\pi r^{2}[/tex]
Simplify
Divide by 8π both sides
[tex]4=r^{2}[/tex]
square root both sides
[tex]r=2\ cm[/tex]
