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#1

Algebra 1 105
Chapter 10 Resource Book
Copyright © McDougal Littell Inc.
All rights reserved.
10.7 Real-Life Application:
When Will I Ever Use This?
For use with pages 619–624
LESSON
NAME _________________________________________________________ DATE ___________
Manufacturing
You work for a company that manufactures round metal washers. The cost to
produce round metal washers is directly related to the amount of metal used.
And the amount of metal used is directly related to the area of the washer, as
shown in the shaded region below.
In Exercises 1-4, use the diagram to the right.

  1. Find the area of the large disc with radius R before the
    middle hole is stamped out. The area of a circle is
    where A is the area and r is the radius of
    the circle.
  2. Find the area of the middle hole with radius r.
  3. Write a formula for the area of the washer that has an
    outer radius R and a hole of radius r, using the formulas
    from parts a and b. Simplify the formula by factoring
    out all common monomial term(s).
  4. You should recognize one of the factors in your formula as a “special product.”
    Show your formula for the area of a washer in yet another form by
    rewriting the “special product” in your formula as two factors.
    In Exercises 5-9, use the following information.
    The process of making this washer starts with a square piece of metal and
    makes two circular stamps. The length of the square’s side will be equal to the
    diameter of the washer (Diameter twice the radius). The material outside the
    diameter of the washer as well as the hole from the middle becomes waste.
  5. Write a formula for the area of the square piece of metal that will be used to
    stamp out the washer.
  6. Create a formula for the amount of metal waste from the production of a
    single washer of outer radius R and inner radius r.
  7. Using your formula from Exercise 3, find the amount of metal used to produce
    a washer with an outer radius of inch and an inner radius of inch.
  8. Find the amount of waste in creating the same washer in Exercise 7.
  9. Comparing the metal wasted to the area of the initial metal square, what
    percent of metal is wasted in creating one of these metal washers?
    1
    2
    3
    4

    A r2, R
    r
    Lesson 10.7
    07-MCRB1-1007-92-106 3-27-2001 8:42 AM Page 105
#2

join to ask for math help
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#3

impressive.

#4

NAME _________________________________________________________ DATE ___________
Real-Life Application:
When Will I Ever Use This?
For use with pages 619–624
Manufacturing
You work for a company that manufactures round metal washers. The cost to produce round metal washers is directly related to the amount of metal used. And the amount of metal used is directly related to the area of the washer, as shown in the shaded region below.

In Exercises 1-4, use the diagram to the right.

  1. Find the area of the large disc with radius R before the middle hole is stamped out. The area of a circle is
    A r2, where A is the area and r is the radius of the circle.
  2. Find the area of the middle hole with radius r.
  3. Write a formula for the area of the washer that has an outer radius R and a hole of radius r, using the formulas from parts a and b. Simplify the formula by factoring out all common monomial term(s).
    LESSON 10.7
    105
  4. You should recognize one of the factors in your formula as a “special product.” Show your formula for the area of a washer in yet another form by rewriting the “special product” in your formula as two factors.
    In Exercises 5-9, use the following information.
    The process of making this washer starts with a square piece of metal and makes two circular stamps. The length of the square’s side will be equal to the diameter of the washer (Diameter twice the radius). The material outside the diameter of the washer as well as the hole from the middle becomes waste.
  5. Write a formula for the area of the square piece of metal that will be used to stamp out the washer.
  6. Create a formula for the amount of metal waste from the production of a single washer of outer radius R and inner radius r.
  7. Using your formula from Exercise 3, find the amount of metal used to produce a washer with an outer radius of inch and an inner radius of inch.
  8. Find the amount of waste in creating the same washer in Exercise 7.
  9. Comparing the metal wasted to the area of the initial metal square, what percent of metal is wasted in creating one of these metal washers?

Copyright © McDougal Littell Inc. Algebra 1 All rights reserved. Chapter 10 Resource Book

#5

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