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.

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) (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
RELATED QUESTIONS
A steel gear is to be lightened by drilling holes through the gear. The gear is 3.27 in.... (answered by Theo)

from a circular sheet of paper of radius 25 cm a sector area 4% is removed. if the... (answered by Theo)

Suppose that you are a mathematician for Well Oils Production ,Inc. Your company is... (answered by psbhowmick,boptop35)

A right circular cylinder of radius r and height h has volume given by V=πr^2h and... (answered by ankor@dixie-net.com)

the surface area of a right circular cylinder with a circular radius r and a height h is... (answered by Fombitz)

Imagine I wrap sheet metal part way around a tube leaving two parallel sides connected by (answered by ikleyn,BM22222)

5 cm. diameter hole is drilled in a 45 cm. by 24 cm. flat rectangular piece of material. (answered by Cromlix)

If 12 men can dig 35 holes in 14 days, (a) how many men are needed to dig 35 holes in 8... (answered by Alan3354,jorel1380)

2. The members of a group of packaging designers of a gift shop are looking (answered by josgarithmetic,MathTherapy)