You are re-tiling the entry to your home and want to create a fancy circular medallion in the center. You want to create a large circle with a smaller circle centered inside. You want to tile the large circle with blue tile and the smaller circle with yellow tile. The circumference of the large circle is 113.097 inches and the radius of the smaller circle is 7 inches. How much blue tile do you need (in square inches)?

You need 864.52 sq. in. of blue tile.

We need to find the area of the large circle (including blue and yellow) and the area of the yellow circle.

We have the circumference of the blue circle, 113.097.
C = πd
113.097 = 3.14d

Divide both sides by 3.14:
113.097/3.14 = 3.14d/3.14
36.018 = d

The diameter is twice as much as the radius, so r = 36.018/2 = 18.009.

The area of a circle is given by the formula
A = πr²
A = 3.14(18.009)² = 1018.38 sq. in.

The area of the small yellow circle is given by
A = 3.14(7²) = 3.14(49) = 153.86

Subtracting these two, we have
1018.38 - 153.86 = 864.52 sq. in.