Circles
A circle is a shape with all points the
same distance from its center.
The distance around a circle is called
its circumference.
The distance across a circle through
its center is called its diameter.
 (pi) is the ratio of the
circumference of a circle to its
diameter. For any circle,
if you divide its circumference by its
diameter, you get a
value close to 3.14159. This
relationship is expressed in the
following formula: C/D = where
C is the circumference and D is the
diameter.
The radius of a circle is the distance
from the center of a circle to a point
on the circle. If you place two radii
end-to-end in a circle, you would
have the same length as one
diameter. So a circle's diameter is
twice as long as its radius.
The formula for the circumference
of a circle is given by either :
C  d or C  2πr
Example : The diameter of a circle
is 3 cm. What is its
circumference? (Use  = 3.14)
Solution: C =  d
C = 3.14 · (3 cm)
C = 9.42 cm
3 cm
Example : The radius of a circle is 2
in. What is its
circumference? (Use = 3.14)
C  2r
C  2  3.14  2
C  12.56in
Example : The circumference of a
circle is 15.7 cm. What is
its diameter? (Use = 3.14)
• C = d
15.7 cm = 3.14 · d
d = 15.7 cm ÷ 3.14
d = 5 cm
The area of a circle is the number of square
units inside that circle. If each square in the
circle below has an area of 1 sq.cm, you
could count the total number of squares to
get the area of this circle. If there were a
total of 28.26 squares, the area of this circle
would be 28.26 csq.m
The area of a circle is given by the
formula
A  r
2
Example : The radius of a circle is 3
in. What is its area?
(Use = 3.14)
•
•
•
•
Solution: A =  · r · r
A = 3.14 · (3 in) · (3 in)
A = 3.14 · (9 sq.in)
A = 28.26 sq.in
Example: The diameter of a circle
is 8 cm. What is its area?
(Use = 3.14)
•
•
•
•
r = 4 cm
A = · r · r
A = 3.14 · (4 cm) · (4 cm)
A = 50.24 sq.cm
Example: The area of a circle is 78.5
sq.m. What is its radius? (Use = 3.14)
•
•
•
•
•
Solution: A = r
2
78.5 sq.m = 3.14 · r
2
78.5 sq.m ÷ 3.14 = r
2
25 sq.m = r
r=5m
2
r 2
Find the area of the rectangular
piece of metal after the 2 circles
are removed.
16 cm
10.00 cm
45.00 cm
28.00 cm
Find the perimeter and area of the
shape.
1
1
P  39.5  C  39.5  C
2
2
P  239.5  C
A  Arect  Acircle
P  79  81.64
A  1557.66in 2
P  79  3.1426.0 
P  160.64in
A  39.526.0  3.1413.0
2
A  1027  530.66
A belt connecting two 9-in-diameter
drums on a conveyor system needs
replacing. How many in long must
the belt be if the centers of the
drums are 10 ft apart? Round to
tenths.
9 in
9 in
10 ft