analytical-geometry-eoct-practice-area-of-a-circle

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This video solves an area word problem in order to show how to answer a free response question on a standardized test.
On the Georgia EOCT it is item 9, the free response.

Billy is creating a circular garden divided into 8 equal sections. The diameter of the garden is 12 feet.

Hi welcome to MooMooMath and today we are going to look at the Georgia Milestones Analytical EOC Assessment Guide
We are looking at some of the free response items I have already done a video on questions 1-4 and 5-8 so this is item 9. This is the first one that is a free response.
Billy is creating a circular garden divided into 8 equal sections. The diameter of the garden is 12 feet.
Let's look and see what we have, and they already have the picture drawn. Here is the circular garden and 8 sections. Lets label our diameter. Our diameter goes all the way across so it will be 12 feet so our radius must be 6. Lets label those two items cause they might be helpful.
What is the area of one section of the garden,explain how you worked it out. Lets work it out and then we go explain it. The area of a circle is Πr^2 The radius is six so lets plug in six which is Π6^2. The area will be 36Π. We know this is the area of the entire circle, but we only want the area of a single slice. There are 8 sections and they are all equal so we will take 36Π and divide it by 8. Lets first reduce the fraction and I can divide both the numerator and denominator by four and that will give me 9Π/2 This is your answer as a fraction. Now lets get a irrational number since pi is irrational because it is not telling us the format to put the answer. So we will put it both ways. 9 x Π / 8 = 3.5325 feet squared because I want to add my units.
Now lets explain what we did.
The first thing we want to do
You want to find the area of the circle by using area = Πr^2
The area is equal to 36Π
The second thing we did was
( and you can write step 2 if you would like)
Step 2 I know that each of the 8 sections are equal have equal areas so I will divide the whole circle area by 8.
36Π/8 = 9/2Π or 3.5 feet
Now explain your answer,so the area of one section is equal to one section can be represented as 9Π/2 square feet or 3.5 square feet.
Remember pi is an exact answer, and your decimal answer is an approximation. So that is how you answer a response which is an open ended question. I have provided a lot of detail and I hope you will also. Hope this video was helpful.

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Please watch: "Study Skills Teacher's Secret Guide to your Best Grades"
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Tagged under: georgia math eoct,area circle,math free response,area circle section,geometry,math

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