Please help, I can't figure this one out. It my last question for my homework and I'm stuck.

First, we need to calculate the areas of both circles, then we can subtract the area of the smaller circle from the area of the larger circle to find out how much tile we need for the blue space.

The circumference of the larger circle is 113.097 square inches. Let's plug this into the formula for the circumference of a circle and solve for the radius(use 3.14 to approximate for pi):

[tex]\sf C=2\pi r[/tex]

Plug in what we know:

[tex]\sf 113.097\approx 2(3.14)r[/tex]

Multiply:

[tex]\sf 113.097\approx 6.28r[/tex]

Divide 6.28 to both sides:

[tex]\sf r\approx 18.01~in[/tex]

Now plug this into the formula for the area of a circle:

[tex]\sf A=\pi r^2[/tex]

[tex]\sf A\approx (3.14)(18.01)^2[/tex]

Simplify exponent:

[tex]\sf A\approx (3.14)(324.3601)[/tex]

Multiply:

[tex]\sf A\approx 1018.491~in^2[/tex]

This is the area of the larger circle, let's find the area of the smaller:

[tex]\sf A=\pi r^2[/tex]

[tex]\sf A\approx (3.14)(7)^2[/tex]

Simplify exponent:

[tex]\sf A\approx (3.14)(49)[/tex]

Multiply:

[tex]\sf A\approx 153.86~in^2[/tex]

This is the area of the smaller circle. Subtract the areas:

[tex]\sf 1018.491-153.86\approx\boxed{\sf 864.631~in^2}[/tex]

So this is how much blue tile you need.