Formulas for Circumference and Area
The formula for the circumference of a
circle is based on the relationship between the
flat surface. (See fig. 17-19.)
The distance from the initial position to the
final position of the disk in figure 17-19 is
approximately 3.14 times as long as the diameter
letter pi. Thus we have the following equations:
Figure 17-18.-Arc, chord, segment, and sector.
Figure 17-19.-Measuring the circumference of a circle.
This formula states that the circumference of a
circle is n times the diameter. Notice that it
could be written as
C = 2r · p
or C = 2pr
since the diameter d is the same as 2r (twice
the radius),
Although the value of p is not exactly equal
to any of the numerical expressions which are
sometimes used for it, the ratio is very close
to 3.14. If extreme accuracy is required, 3.1416
is used as an approximate value of p. Many
calculations involving p are satisfactory if the
fraction 22/7 is used as the value of p.
Practice problems. Calculate the circumference of each of the following circles, using
22/7 as
the value of p:
1. Radius = 21 in.
2. Diameter = 7.28 in.
3.
Radius = 14 ft
4. Diameter = 2.8 yd
Answers:
1. 132 in.
2. 22.88 in.
3. 88 ft
4. 8.8 yd
AREA.-The area of a circle is found
formula is written as follows:
A = pr2
EXAMPLE: Find the area of a circle whose
diameter is 4 ft, using 3.14 as the value of
p.
SOLUTION: The radius is one-half the diameter. Therefore,
Practice problems. Find the area of each of
the following circles, using 3.14 as the value of
p.
1. Radius = 7 in.
2. Diameter = 42 mi
3. Diameter = 2.8 ft
4.
Radius = 14 yd
Answers:
1. A = 154 sq in.
2. A = 1,385 sq
ml
3. 6.15 sq
ft
4. 615 sq
yd
Concentric Circles
Circles which have a common center are
said to
CONCENTRIC.
(See fig. 17-20.)
The area bf the ring between the concentric circles in figure 17-20 is calculated as follows:
Figure 17-20.-Concentric circles.
Notice that the last expression is the difference
of two squares. Factoring, we have
A = p(R + r)(R - r)
Therefore, the area of a ring between two
circles is found
by p
times the product of the sum and difference of their radii.
Practice problems. Find the areas of the rings
the
following concentric circles:
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