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jbarber
Group Title
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
 2 years ago
jbarber Group Title
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
 2 years ago

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

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

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

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

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

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