Nada is making square coasters with sides of 3 inches. on each coaster is a circular design. what is the radius of the largest circle that fits on one of the coasters?

2.25π square inches [or 7.07 sq. in. rounded to 2 decimal places]

Step-by-step explanation:

The largest circle inscribed in a square would have DIAMETER EQUAL TO THE SIDE LENGTH OF THE SQUARE.

Since diameter is double of radius, we can find the radius to be:

diameter = 3 [side length of square]

radius = 3/2 = 1.5 inches

The area of a circle is  πr^2

THus, the largest circle area = πr^2 = π(1.5)^2 = π(2.25) = 2.25π square inches