Kyle R. answered • 02/27/16

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Mathematics and Science Tutor - Graduate Student

This problem is asking for the area of the tire, so we need to find the area of the outer circle of the tire and then subtract the area of the inner wheel.

The area of a circle is represented by the equation, A = πr

^{2}(r = radius of the circle).We can find the area of the outer circle of the tire by using the radius, which is half of the diameter, squaring it, and then multiplying it by π:

A = π(4.5)

^{2}A = 20.25π

Now, we can find the area of the inner wheel by knowing that the circumference of a circle is represented by the equation, C = 2πr. Because we know C = 2πr, we can solve for the radius:

6π = 2πr

6 = 2r

3 = r

So, the radius of the inner wheel is 3 cm. We can now use this radius to find out the area of the inner wheel:

A = π(3)

^{2}A = 9π

To find the area of the tire, we just have to subtract the area of the inner wheel from the area of the outer circle:

A = 20.25π - 9π

A = 11.25π

If we use 3.14 for π, then the area of the tire is 11.25(3.14) = 35.325 cm

^{2}.Kyle R.

Yes, I agree as well, but I simplified it for the OP. I'm assuming they are either in elementary or middle school, so I didn't feel the need to complicate it beyond the process of finding the answer.

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02/27/16

Kenneth S.

02/27/16