SOLUTION: A machine shop needs to make a small automotive part by drilling four holes of radius r from flat circular piece of radiusR. The area of the resulting part is eight square inches.

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Question 872322: A machine shop needs to make a small automotive part by drilling four holes of radius r from flat circular piece of radiusR. The area of the resulting part is eight square inches. Write an equation that relates r and R.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The big circle has an area of pi*R^2

The small circles have individual areas of pi*r^2 and there are 4 of them, so they total to 4*pi*r^2

(Area of Big circle) - (Area of little circles) = Resulting area

pi*R^2 - 4*pi*r^2 = 8

you can optionally factor out pi to get

pi*(R^2 - 4r^2) = 8

and then factor the remaining bit using the difference of squares rule to get

pi*(R - 2r)*(R + 2r) = 8