Question

I have a circle with a hole i.e. a washer
hole or inner circle has a radius of R. The washer has a width of W. What is the area of the washer?

Answer 1

The description is a little strange.
Do you mean like this?

Answer 2

yes exactly sorry hard to explain

Answer 3

Find the area of the larger circle, subtract from it the area of the inner circle.

Answer 4

\[
\text{Area of washer = } \pi \{r_{\text{outer}}^2 - r_{\text{inner}}^2\} = \pi\{(R+W)^2 - R^2 \}
\]

Answer 5

You'll need to find the larger radius to be able to do that :)

Answer 6

\[
\pi\{(R+W)^2 - R^2 \} = \pi(R+W+R)(R+W-R) = \pi (2R+W)(W) = \pi W(2R+W)
\]

Answer 7

when you say "The washer has a width of W", do you mean this?

Answer 8

or do you mean this?

Answer 9

ok, then you'll use aum's formula

Answer 10

Im following the equation aum gave. But I am confused as to how I get the 2nd part
\[\pi(R+W+R)(R+W-R)\]

Answer 11

aum used the difference of squares formula to factor (R+W)^2 - R^2

Answer 12

a^2 - b^2 = (a+b)(a-b)

in this case

a = R+W
b = R

Answer 13

thank you