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)

I just need someone to explain how to solve this please!!

Since you have the circumference of the large circle, you can easily find the radius of the large circle using the formula for the area of a circle. You can then use this information to find the area of the large circle and subtract the area of the smaller circle in order to get the area of the blue section. Hope this makes sense.

To find the area of the blue tile you will potentially need for your circular medallion, you first need to determine the area of the large circle.

The circumference of a circle (C) is given by the formula C = 2πr, where r is the radius of the circle. You already have the circumference (113.097 inches), so you can rearrange the formula to solve for the radius (r): r = C / (2π). Plugging in the given circumference, you get r = 113.097 / (2π).

Once you've obtained the radius of the large circle, you can find its area (A) with the formula A = πr^2, where r is the radius. Simply square the radius value you obtained earlier and multiply it by π to calculate the area of the large circle.

Now, to determine the area of the smaller circle, you can directly use the formula A = πr^2, where r is the radius of the smaller circle (which is given as 7 inches). Plug in the given value and calculate the area.

After obtaining the areas of both the large and the small circles, you can subtract the area of the smaller circle from the area of the larger circle to find the area of the blue tile needed. This is because the area of the blue tile corresponds to the difference in areas between the two circles.

I hope this explanation helps you solve the problem!