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 2 years ago
A machinist creates a washer by drilling a hole through the center of a circular piece of metal. If the piece of metal has a radius of x + 10 and the hole has a radius of x + 6, what is the area of the washer?
 2 years ago
A machinist creates a washer by drilling a hole through the center of a circular piece of metal. If the piece of metal has a radius of x + 10 and the hole has a radius of x + 6, what is the area of the washer?

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richyw
 2 years ago
Best ResponseYou've already chosen the best response.0ok so you have two circles. The area of the washer is the area of the piece of metal minus the area of the hole.\[A_{washer}=A_{metal}A_{hole}\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0both are circles and the area of a circle with radius \(r\) is \(A=\pi r^2\)

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0so let \(r\) be the radius of the hole, and \(R\) be the radius of the metal. Then you have\[A_{washer}=\pi R^2\pi r^2=\pi\left(R^2r^2\right)\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0Ok so from here there are a few ways you can go. I prefer just to plug in the values, expand it out, and simplify\[A_{washer}=\pi\left((x^2+20x+100)(x^2+12x+36)\right)\]\[A_{washer}=\pi\left(20x+10012x36\right)\]\[A_{washer}=\pi\left(8x+10036\right)\]\[A_{washer}=\pi\left(8x+64\right)\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0\[A_{washer}=8\pi(x+8)\]

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0this is of course assuming that the washer is 2D.
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