Basic Mathematics for College Students

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APPLICATIONS

51. Suppose the two “legs” of the compass shown below
    are adjusted so that the distance between the pointed
    ends is 1 inch. Then a circle is drawn.
    a. What will the radius of the circle be?
    b. What will the diameter of the
    circle be?
    c. What will the circumference
    of the circle be? Give an
    exact answer and an
    approximation to the nearest
    hundredth.
    d. What will the area of the
    circle be? Give an exact
    answer and an approximation
    to the nearest hundredth.


52. Suppose we find the distance
    around a can and the distance
    across the can using a measuring
    tape, as shown to the right. Then
    we make a comparison, in the
    form of a ratio:

After we do the indicated division, the result will be

close to what number?

When appropriate, give the exact answer and an approximation

to the nearest hundredth. Answers may vary slightly, depending

on which approximation of pis used.

53. LAKES Round Lake has a circular shoreline that is
    2 miles in diameter. Find the area of the lake.


54. HELICOPTERS Refer to the figure below. How far
    does a point on the tip of a rotor blade travel when it
    makes one complete revolution?


55. GIANT SEQUOIA The largest sequoia tree is the
    General Sherman Tree in Sequoia National Park in
    California. In fact, it is considered to be the largest
    living thing in the world. According to the Guinness
    Book of World Records,it has a diameter of 32.66 feet,
    measured feet above the ground. What is the
    circumference of the tree at that height?

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The distance around the can

The distance across the top of the can

56. TRAMPOLINE See the figure below. The distance
    from the center of the trampoline to the edge of its
    steel frame is 7 feet. The protective padding covering
    the springs is 18 inches wide. Find the area of the
    circular jumping surface of the trampoline, in square
    feet.


57. JOGGING Joan wants to jog 10 miles on a circular
    track mile in diameter. How many times must she
    circle the track? Round to the nearest lap.


58. CARPETING A state capitol building has a circular
    floor 100 feet in diameter. The legislature wishes to
    have the floor carpeted. The lowest bid is $83 per
    square yard, including installation. How much must
    the legislature spend for the carpeting project?
    Round to the nearest dollar.


59. ARCHERY See the figure
    on the right. Find the area of
    the entire target and the
    area of the bull’s eye.
    What percent of the
    area of the target is the
    bull’s eye?

60. LANDSCAPE DESIGN

See the figure on the

right. How many square

feet of lawn does not get

watered by the four

sprinklers at the center of

each circle?

WRITING

61. Explain what is meant by the circumference of
    a circle.


62. Explain what is meant by the area of a circle.


63. Explain the meaning of p.


64. Explain what it means for a car to have a small
    turning radius.

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Protective

pad

800 Chapter 9 An Introduction to Geometry

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30 ft