14.5 Circumference of a Circle
Common Core Standards
7.G.2. Draw (freehand, with ruler and protractor, and with technology)
geometric shapes with given conditions. Focus on constructing
triangles from three measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one triangle, or no
triangle.
7.G.4. Know the formulas for the area and circumference of a circle and
use them to solve problems; give an informal derivation of the
relationship between the circumference and area of a circle to write and
solve simple equations for an unknown angle in a figure.
7.G.5. Use facts about supplementary, complementary, vertical, and
adjacent angles in a multi-step problem to write and solve simple
equations for an unknown angle in a figure.
WARM-UP
1) What is the length of the diameter of the circle?
8 in
6 in
Circumference of a Circle
How do we find the length around the
outside of a circle?
NOTES
The diameter of a circle is a segment from the edge of
a circle to the opposite side through the center.
The radius is a segment from the center to the edge.
A chord is any segment connecting two points along
the edge (not through the center).
Examples
Find the diameter and radius of the circle.
NOTES
The circumference of a circle is the length around the
edge. There is a special relationship between the
diameter of every circle and its circumference.
Circumference
= 3.1415926... = π
diameter
Examples
Divide the circumference by the diameter.
Circumference = 22 cm
NOTES
So we can approximate the length of the circumference
using the formula…
C = π gd
C ≈ 3.14gd
C = circumference
d = diameter
Examples
Approximate the circumference using 3.14 for π .
NOTES
If we want our answer to be exact, we have to leave pi
in our answer.
Examples
Find the exact circumference.
4.6
cm
8 in
NOTES
The diameter is always twice the radius.
Examples
Approximate the
circumference using 3.14
for π .
3 ft
Find the exact
circumference.
EXAMPLES
Quickly approximate which number is closest to the
circumference.
a)  9 in
12 in
b)  17 in
6 in
c)  25 in
d)  38 in
PRACTICE
Write the formula for the circumference of a circle.
Approximate the
circumference using
3.14 for π .
8.25"
Find the exact
circumference.
7 cm
FINAL QUESTION
Find the exact circumference.
2.25'