What you're looking for here is the surface area of the sides of the glasses (what the koozies will cover). This is also what the amount represents.
The surface area of the sides is equal to the perimeter of the base times the height of the cylinder. It makes sense logically because the sides are basically the perimeter of the base, raised all the way up along the cylinder.
SA = perimeter x height
SA = pi x diameter x height
SA = 3.14 x 3in x 4in
SA = 37.68 in^2
She will use 37.68 square inches of fabric.