Basic Mathematics for College Students

9.8 Circles 795

We then change the 25 miles to inches using two unit conversion factors.

The units of miles

and feet can be

removed.

The length of the trip is inches.

Finally, we divide the length of the trip by the circumference of the tire to get

We can use a scientific calculator to make this calculation.

25 5280 12 15

The tire makes about 33,614 revolutions.

(   )  (  p )  33613.52398

The number of

revolutions of the tire



25 5,280 12

15 p

25 5,280 12

25 miles

1



5,280 feet

1 mile



12 inches

1 foot

 25 5,28012 inches

EXAMPLE (^2) Architecture A Norman window
is constructed by adding a semicircular window to the top of
a rectangular window. Find the perimeter of the Norman
window shown here.
StrategyWe will find the perimeter of the rectangular part
and the circumference of the circular part of the window
and add the results.
WHYThe window is a combination of a rectangle and a
semicircle.
SolutionThe perimeter of the rectangular part is
Add only 3 sides of the rectangle.
The perimeter of the semicircle is one-half of the circumference of a circle that has
a 6-foot diameter.
This is the formula for the circumference of a semicircle.
Since we know the diameter, replace Cwith PD. We could
also have replaced Cwith 2Pr.
Substitute 6 for D,the diameter.
Use a calculator to do the multiplication.
The total perimeter is the sum of the two parts.
To the nearest hundredth, the perimeter of the window is 31.42 feet.

31.424777961

Ptotal 22 9.424777961

PtotalPrectangular partPsemicircle

9.424777961



1

2

p( 6 )

Psemicircle

1

2

pD

Psemicircle

1

2

C

Prectangular part 8  6  8  22

8 ft 8 ft

6 ft

3 Find the area of a circle.

If we divide the circle shown in figure (a) on the following page into an even number
of pie-shaped pieces and then rearrange them as shown in figure (b), we have a figure
that looks like a parallelogram. The figure has a base that is one-half the
circumference of the circle, and its height is about the same length as a radius of
the circle.

h

b

Self Check 2

Find the perimeter of the figure

shown below. Round to the

nearest hundredth. (Assume the

arc is a semicircle.)

Now TryProblem 29

12 m

3 m

12 m