Q:

Please help and explain how to get the answer! I just need to know how to do itYou 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)?

Accepted Solution

A:
You need 864.518 in² of blue tile.

We use the circumference to find the diameter of the blue circle.  The formula for circumference is C=πd:

113.097=3.14d

Divide both sides by 3.14:
113.097/3.14 = 3.14d/3.14
36.018 = d
This is the diameter of both circles together.

The radius of the entire circle is 1/2 of the diameter:
36.018/2 = r
18.009 = r

We find the area of the entire circle using the formula
A = πr²
A=3.14(18.009)² = 1018.378

Now we find the area of the yellow circle:
A = 3.14(7²) = 153.86

The area of the blue circle is the total area minus the area of the yellow circle:
1018.378-153.86 = 864.518