Geometry – Circles

Circles are shapes made up of all points in a plane
that are the same distance from a point called the
center.

Look at this example of a circle:
center
diameter – the distance
across a circle through
its center
circumference - the
distance around a circle
radius – the distance
from the center to any
point on a circle

What is the distance around the circle?

How much space is inside the circle?

The distance around the circle is called the
circumference.

The space is inside the circle is called the area.


The circumference of every circle is
approximately three times longer than its
diameter!
C
This relationship (
) is where π or pi comes
d
from.

To find the circumference or area of a circle,
you must use this relationship or the value pi.

22
Pi ≈ 3.14 or
7

You may use whichever form you wish.

If your problem contains multiples of seven
(7), it makes sense to use the fractional form
of pi.

You will always be given the circle’s diameter or
the radius.

Your answer will be a linear measurement.

The radius is always

½ of the diameter.
The diameter is always
radius.
diameter – the distance
across a circle through
its center
two times
the
radius – the distance
from the center to any
point on a circle

The circumference formulas are found on the
key of the FCAT Reference Sheet.

Choose the correct formula for circumference.
Use this
formula if
you have
diameter (d)
Use this
formula if
you have
radius (r)



Write the circumference formula exactly as it
appears on the FCAT Reference Sheet.
Rewrite the circumference formula
substituting the values that you know.
Solve one step at a time rewriting after each
step.
C = Πd
C = 3.14 × 12
A = 28.26 meters



Write the circumference formula exactly as it
appears on the FCAT Reference Sheet.
Rewrite the circumference formula
substituting the values that you know.
Solve one step at a time rewriting after each
step.
C = 2Πr
C = 2 × 3.14 × 12
A = 75.36 meters

Follow the same set of steps as before!
 Write the circumference formula exactly as it appears
on the FCAT Reference Sheet.
 Rewrite the circumference formula substituting the
values that you know.
 Solve one step at a time rewriting after each step.

Solve the following problem:
 Find the diameter of a basketball hoop with a
circumference of 56.52 inches. Use 3.14 for Π.
C
56.52
18 in.
= Πd
= 3.14 × d
Divide by 3.14 on both sides to
undo the multiplication!
=d
1. One is on the left.
50 m
14 m
2. One is on the right. Note: Use
22
7
for Π.
1. C = Πd
22
2
4. C =
×
1
1
22
2. C =
× 14
7
5. C =
22
14
3. C =
×
7
1
6. C = 44 meters
Since you are finding
two halves, you can
find one whole instead!
44
1
50 m
14 m


You will always be given the circle’s diameter,
radius, or its circumference.
You need to find the value of radius before you
begin!
½ of the diameter or r = d ÷ 2.

The radius is always

The diameter is equal to circumference divided by pi or
3.14. Or d =

C
3.14
Sometimes you are given radius. This means less work!!

Select the correct area formula:



Write the area formula exactly as it appears
on the FCAT Reference Sheet.
Rewrite the area formula substituting the
values that you know.
Solve one step at a time rewriting after each
step.
2
12 mm
A = Πr
A = 3.14 × r × r
A = 3.14 × 12 × 12
A = 3.14 × 144
A = 452.16 mm2



Write the area formula exactly as it appears
on the FCAT Reference Sheet.
Rewrite the area formula substituting the
values that you know.
Solve one step at a time rewriting after each
step.
A = Πr2
r=d÷2
A = 3.14 × r × r
r=6÷2
A = 3.14 × 3 × 3
r=3
A = 3.14 × 9
A = 28.26 ft2
6 feet




Write the area formula exactly as it appears on
the FCAT Reference Sheet.
Rewrite the area formula substituting the values
that you know.
Solve one step at a time rewriting after each
step.
Divide your answer by 2!
Note: You could also use the formula
or
4 inches




Remember to multiply by ½ or divide by 2!
Choose the formula that you feel the most
comfortable using.
You are finding the area of one half of a
circle!
You can use this same method to find the
circumference of one half of a circle!



Remember that the shapes have two
dimensions.
When you multiply one measurement by
another measurement you end up with square
units.
For Example:
•Square Feet
•ft2
•Square Inches •Square Centimeters
•in2
•cm2

Remember to use the FCAT Reference Sheet: