Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jbarber

  • 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?

  • This Question is Closed
  1. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 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. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    both are circles and the area of a circle with radius \(r\) is \(A=\pi r^2\)

  3. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so let \(r\) be the radius of the hole, and \(R\) be the radius of the metal. Then you have\[A_{washer}=\pi R^2-\pi r^2=\pi\left(R^2-r^2\right)\]

  4. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 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\[A_{washer}=\pi\left((x^2+20x+100)-(x^2+12x+36)\right)\]\[A_{washer}=\pi\left(20x+100-12x-36\right)\]\[A_{washer}=\pi\left(8x+100-36\right)\]\[A_{washer}=\pi\left(8x+64\right)\]

  5. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[A_{washer}=8\pi(x+8)\]

  6. richyw
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this is of course assuming that the washer is 2D.

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.