Unit 4 Circles and Area
Parts of a Circle
The distance from the center of the circle to any
point on the circle is called the radius
(symbol is r).
r
More than one radius is called radii.
A line passing through the center of the circle
with both endpoints on the circle is called the
diameter (symbol is d).
r
Center
r
1.
d
Notice that one diameter equals two radii.
d=2xr
d = 2r
Find the diameter.
A)
B)
3.2 cm
4 cm
Diameter = 4 x 2
= 8cm
C)
Radius = 6cm
Diameter = 6 x 2
= 12cm
Diameter = 3.2 x 2
= 6.4cm
D)
Radius = 10.5 cm
Diameter = 10.5 x 2
= 21cm
B)
1 0
c m
A)
c m
Find the radius.
Center
d
d
=
=
Center
Radius = 10 ÷ 2 = 5cm
C)
Radius = 16.2 ÷ 2 = 8.1cm
Diameter = 15cm
Radius = 15 ÷ 2 = 7.5cm
Note:
1 6
.2
2.
D) Diameter = 14.6 cm
Radius = 14.6 ÷ 2 = 7.3 cm
d  2r
If diameter = 2 x radius
then radius = diameter ÷2
r  d  2 or r 
3.
A)
d
2
A circle has a radius of 1.7cm. What is the diameter of the
circle?
1.7 x 2 = 3.4cm
Diameter is 3.4cm
B)
4.
A circle has a diameter of 8.6cm. What is the radius of the
circle ?
r = d ÷2
r = 8.6 ÷ 2
radius = 4.3cm
An artist has a sheet of poster paper measuring 1.6m by 2.2m as
shown. What is the radius of the largest circle that can be cut
from the paper?
2.2 m
Diameter = 1.6
1.6 m
So radius = 1.6 ÷ 2
= 0.8 m
Practice
1:
Find the diameter of the circle with each radius.
A)
2:
r = 12 cm
12 x 2
24cm
B)
r = 27 cm
27 x 2
54cm
C) r = 3.4 cm
3.4 x 2
6.8cm
Find the radius of the circle with each diameter.
A)
d = 12 cm
12 ÷ 2
6cm
B)
d = 27 cm
27 ÷ 2
13.5cm
C)
d = 3.4 cm
3.4 ÷ 2
1.7cm
3.
Circular plates with diameter 20cm are placed side by side on
a table. The table measures 2.4m by 1.2 m.
(Tip: To convert meters to centimeters multiply by 100)
A)
What is the length of the table in centimeters?
2.4 x 100 = 240cm
B)
How many plates can fit side by side along the length of the
table?
240 ÷ 20 =12 plates
C)
What is the width of the table in centimeters?
1.2 x 100 = 120
D)
How many plates can fit side by side along the width of the
table?
120 ÷ 20 = 6 plates
E)
How many plates can fit on the table?
6 x 12 = 72 plates
F)
How many plates can fit around the perimeter of the table?
6 + 6 + 12 + 12 = 36
However, each corner would have double plates so
36 – 4 = 32
Constructing Circles
You can construct a circle using a compass and a ruler.
Examples
1:




Draw a circle with a radius of 2cm.
Make dot on your paper. This will be the center of your circle.
Using your compass and ruler, open your compass to 2cm.
Place the pointy end of the compass on the dot, and draw your
circle.
You can measure the radius of your circle with your ruler to
check to see if it’s accurate.
TRY IT
2.
Draw a circle with a diameter of 6cm.
Tip: Find the radius first and follow the same steps!
You could also trace objects to create circles.
Find TWO circular objects and practice tracing circles.
Object # 1
Circle Activity
Object # 2
Each person was asked to bring in 3 circular objects of different sizes.
You will also need a string, ruler and a calculator.
Directions:
*
Work with a partner
*
Put all the circular objects on your desk
*
Record the names of your objects, i.e. Campbells soup, Pringles
chips, etc...
*
Use the string to measure the distance around each object
(perimeter)
*
Use the ruler to measure the diameter.
*
Calculate the radius from the diameter.
*
Use the calculator to determine the distance around divided by
the diameter.
Object
Distance Around Diameter
Radius
Distance Around
the Object (cm)
÷ Diameter
(cm)
(cm)
Coffee cup
19cm
6cm
3cm
19 ÷ 6 = 3.16
Counter
8cm
2.5
1.25cm
8 ÷ 2.5 = 3.2
Questions
1:
What do you notice about the answers in column 5?
All numbers were close to the digits of pi (3.14)
2:
Does the size of the circle affect the answers?
No!
3:
Write an equation to find the distance around any circle.
3.14 x diameter so ∏d