Question

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)?

Answer 1

Are needed
`863.5\ in^(2)` of blue tile

Explanation:

we know that

To find how much blue tile do you need, subtract the area of the smaller circle from the area of the large circle

step 1

Find the radius of the large circle

The circumference of the circle is equal to

`C=2\pi r`

we have

`C=113.097\ in`

substitute and solve for r

`113.097=2\pi r`

`r=113.097/(2\pi)`

assume

`\pi=3.14`

`r=113.097/(2(3.14))=18\ in`

step 2

Find the area of the large circle

`A=\pi r^(2)`

we have

`r=18\ in`

substitute

`A=\pi (18)^(2)=324\pi\ in^(2)`

step 3

Find the area of the smaller circle

`A=\pi r^(2)`

we have

`r=7\ in`

substitute

`A=\pi (7)^(2)=49\pi\ in^(2)`

step 4

Find the difference of the areas

`324\pi\ in^(2)-49\pi\ in^(2)=275\pi\ in^(2)`

assume

`\pi=3.14`

`275(3.14)=863.5\ in^(2)`