Http://. For Learning to Happen: Pay close attention to this lesson. Listen to my instructions to discover the area of a circle

http://www.mathslideshows.com


For Learning to Happen:

•Pay close attention to this lesson.•Listen to my instructions to discover the area of a circle formula.


• You are going to get a white half sheet.

• Label the circumference, diameter and radius on your circle.


DiameterRadius

•Carefully cut out the circle on the black line.


•Cut out the circle on the bolded lines.

•Cut along the diameter to cut the circle in half.

• You should have 2 halves.


• Start from the diameter and cut the 4 pieces.

• DO NOT CUT IT TO THE EDGE!

•Open the semicircles and bend them out so they look like 4 connected triangles.


• Fit the 4 triangles together so that as one is facing up, the other is facing down.

• Tape these pieces together on your blue study guide handout.

• Make sure your words on facing up!

Circumferenceradiu

s


Answer the following questions. 1. What does your new figure look like? Parallelogram2a. Draw your answer here. Label base & height

2b. How do you find the area of a parallelogram? Base x Height

base

height


3. Draw your area of a circle figure below. In knowing that you need to find the base and height of your new figure to calculate the area, what is the height of your new figure? Label your picture.

4. What is the bottom base of your new figure? Label your picture above. Hint: Half of the circumference.

Height = radius

pi x radius

C = πd C = 2πr


5. If you know the base and height of your new figure can you find the area? Take your base and multiply it by your height. Show your work!

6. Simplify your formula.

7. Write out how you find the area of a circle.

Pi times radius squared.

r

r

πr • r2A = πr


Here is what we just did:

C d We cut our circlein half making two pieces.

radius

Circumference is the distance around the circle.

We labeled everything.

r

C 2 r r

r

r

Area = base times the height.

A r r 2A r


r

rC 2 r

Watch what happens when we use a circle with 16 triangles instead of using a circle with 8 triangles.

r

r

Notice that with more triangles the figure begins to really resemble a parallelogram. Area of a parallelogram is base times height.

2A r


Take out a calculator to try to solve the following problems on area of a circle.


Find the area of the circle.

6 in.

2A r 26A ( )

A 36 A 36

2A 113.09 in



11 m.

2A r 2A ( 1)1

A 121 A 121

2A 380.13 m



10 ft.

2A r 25A ( )

A 25 A 25

2A 78.53 ft

What is the radius if the diameter is 10 ft?


The End!

Take out your study guide!


6 in

= 3.14 or 22 7

#7

A = π radius squared2A = πr

2A = (3.14)6

A = (3.14) 36

2A = 113.04 in

copyright©amberpasillas2010


#8

Find the Circumference

5 ft

Find the AreaC = 2 rC = 2 5

C = 31.42 ft

Round to the nearest hundredths place and include units!

2A = r2A = 5

A = 252A = 78.54 ft

C = 10

copyright©amberpasillas2010



Use this as a master to give to studentsfor the interactive discovery of a circle along with a copy of the worksheet.

Student materials for interactive discovery of a circle: Copy of circle pictured above, copy of area worksheet in this folder, scissors & tape.


Area of a CircleFollow the teacher directions and cut the circle out.

Area of a CircleFollow the teacher directions and cut the circle out.


TEACHER NOTE: Give each student a copy of this page. The master copy is in the folder as a pdf.

Documents

Http://. For Learning to Happen: Pay close attention to this lesson. Listen to my instructions to discover the area of a circle