First mug holds the most
Solution:
Given that,
You are choosing between two mugs
The volume of cylinder is given as:

Where,
r is the radius and h is the height
One has a base that is 5.5 inches in diameter and a height of 3 inches

Therefore,

Also, h = 3 inches
Thus volume of cylinder is given as:

Thus first mug holds 71.24 cubic inches
The other has a base of 4.5 inches in diameter and a height of 4 inches

h = 4 inches
Therefore,

Thus the second mug holds 63.585 cubic inches
On comparing, volume of both mugs,
Volume of first mug > volume of second mug
First mug holds the most