Since I'm an engineer, I had to sketch it out:
D, diameter of the outer circleGiven
R, radius of the outer circle
d, diameter of the inner circle
r, radius of the inner circle
C, length of chord tangent to the inner circle
C = 70 ftExamining Figure 1, we see that r intersects C at its midpoint. Therefore,makes up one leg of a right triangle with r and R. The Pythagorean Theorem relates the three sides of a right triangle as
Substituting in our variables yields
Which can be rearranged as
Now we have one equation but two unknown variables. Let’s establish some relationships for area. The generalized equation for the area of a circle is
In terms of the outer circle
In terms of the inner circle
To solve the problem, we must find the area between the circles:
Recall from our Pythagorean relationship that we (rather fortunately) know the value of (R2-r2).
Ed, Biff, and Skip need enough paint to cover 3,846.5 square feet.