1. April 9, Math 201
OBJECTIVE: Students will be able to determine the area of a circle and the area of a sector of a circle.
AIM: How will our knowledge of proportions help us find the area of a sector of a circle?
STANDARDS: 6.G.7, 6.G.8
PRIOR KNOWLEDGE: If Richie rides his bike and goes 8 miles in 2 hours, how many miles will Richie ride in 6 hours? Use proportional reasoning to solve.

2. Sector
Central Angle A C B

3. The area of the sector of the circle can be found by using a proportion:
Measure of central angle = area of the sector
area of the circle

4. A slice of pizza is a sector of a circle!!
10 cm
45 degrees
Mr. Brooks’ Uncle Luigi cuts a nice slice of pizza in his restaurant near Rome. Given the information in the diagram, how many square cm is the slice?

5. Formula
Measure of central angle = area of the sector
area of the circle
First find the area of the circle
A = πr2
= π(102)
= 100π

6. Substituting values into the formula
45 = area of the sector π
Simplify your fraction, if possible
So,
1 = area of the sector π
Cross multiply
8 x area of the sector = 100π
area of the sector = 100π 8
So,
area of the sector = 12.5π cm

7. 8 x area of the sector = 100π
DIVIDE EACH SIDE THROUGH BY 8
8 X area of the sector = 100π
So,
area of the sector = 100π = 12.5π cm 8

8. “Can I have a sector with an area of
The next time you are out for a slice, try asking the pizza guy:
“Can I have a sector with an area of
about 15 sq cm?”
And see what he says!