A circular coaster, with a diameter of 7 inches, is positioned on a white placement. The placement is a circle whose radius is equal to the diameter of the coaster. About how many square inches of the placemat are NOT covered by the coaster? Show your work.

It would help if you proofread your questions before you posted them.

I assume that all of your "placements" are really placemats.

Area = π * r^2

d = 2r

Area of coaster = π * 3.5^2

Area of placemat = π * 7^2

Subtract area of coaster from area of placemat.

To find the area of the placemat that is not covered by the coaster, we need to subtract the area of the coaster from the area of the placemat.

Let's find the area of the coaster first. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

The diameter of the coaster is given as 7 inches, so the radius would be half of that, which is 7/2 = 3.5 inches.

Using the formula for the area of a circle, we find that the area of the coaster is A_coaster = π(3.5)^2.

Now, let's find the area of the placemat. The radius of the placemat is equal to the diameter of the coaster, which is 7 inches.

Using the formula for the area of a circle, we find that the area of the placemat is A_placemat = π(7)^2.

To find the area of the placemat that is not covered by the coaster, we subtract the area of the coaster from the area of the placemat:

A_not_covered = A_placemat - A_coaster

Calculating the areas:
A_coaster = π(3.5)^2 = 38.465 square inches (rounded)
A_placemat = π(7)^2 = 153.935 square inches (rounded)

Now, subtracting the area of the coaster from the area of the placemat:
A_not_covered = 153.935 - 38.465 = 115.47 square inches (rounded)

Therefore, about 115.47 square inches of the placemat are not covered by the coaster.