.The area of a circle is ___________________________________.
Describe how area and circumference are different:____________________
_____________________________________________________________.
The formula for the area of
a circle is A = .
Assignment #9:
1.) Open up GSP and construct a circle. Find the area and circumference of your circle. Print out the circle.
2.) Construct another circle and find the arc length of your circle when the arc measure is 60 degrees and the radius 4 units.
Print out the circle.
What is a sector of a circle? Let's look at a picture:
A sector is similar to a piece of a pie. Can you think of anything else a sector might look like in the real world?
The sector above has an arc measure of ______ and a radius of ______.
We could easily find the arc length from A to B. -Find it!
To find the area of the sector, it is going to be a portion of the area of the circle.
We will use a proportion to find this,
we know 
so, 
Class activity:
Construct your own sector and find the area of it. Compare the area of the sector to the area of the circle.
Trade with your neighbor when you are finished and complete their problem as well.
1.) Draw in a piece of pie that you want to eat.
2.) Measure the arc measure or central angle of your piece of pie.
3.) Measure the radius of your piece of pie in millimeters.
4.) Find the area and circumference of the whole pie.
5.) Find the area and arc length of your piece of pie.
6.) Trade drawings with your partner and check each others calculations and measurements.
7.) Discuss with your partner a word problem that could be written from both of your pies.
8.) Write one word problem for the both of you. Be prepared to present and explain it to the class.
The Broken Plate Problem:
You went on vacation to The Dominican Republic with your family and spent a day in Santo Domingo. You were walking down an ancient street and saw something protruding from a sand pile. You dug it up and found a broken plate. It looked extremely interesting and had beautiful geometric designs on it, but you could not see all of it since it was broken and was the same size as the picture above. Your parents begged you to take it to the local store because it looked like an heirloom. When you took it there they said it was over 500 years old. You said, "wow!" The store clerk told you that archeaologists had been looking for that plate for a long time because it may have belonged to Christopher Columbus. The store clerk tells you that if you can find how big the plate actually was then the archaologosts will pay you 100 dominican pesos. So you need to get to work because you ran out of vacation funds the first day of vacation!
1.) Figure out the archeaologists problem.
2.) Contiue with you exploation and explain how you would come up with the area of the broken piece. Then find that area.
3.) Make a geometrical design on the finished plate to represent your vision of how it looked.
4.) Collect your 100 dominican pesos. How much is that in American money?