Answer:
see the explanation
Step-by-step explanation:
we know that
The volume of a cylinder (a mug) is equal to
[tex]V=\pi r^{2} h[/tex]
where
r is the radius of the base
h is the height
step 1
Find the volume of the one mug
we have
[tex]r=5.5/2=2.75\ in[/tex] ---> the radius is half the diameter
[tex]h=3\ in[/tex]
substitute
[tex]V=\pi (2.75)^{2} (3)[/tex]
[tex]V=22.69\pi\ in^3[/tex]
step 2
Find the volume of the second mug
we have
[tex]r=4.5/2=2.25\ in[/tex] ---> the radius is half the diameter
[tex]h=4\ in[/tex]
substitute
[tex]V=\pi (2.25)^{2} (4)[/tex]
[tex]V=20.25\pi\ in^3[/tex]
step 3
Compare the volumes
[tex]22.69\pi\ in^3 > 20.25\pi\ in^3[/tex]
therefore
The mug with the greatest volume is the one that holds the most
