How to calculate the area of a circle.: How to calculate the area of a circle. It’s as easy as pi.
Let’s first make sure that we understand the difference between circumference and area.: Let’s first make sure that we understand the difference between circumference and area.
The circumference of a circle is the perimeter of the circle. : The circumference of a circle is the perimeter of the circle.
Imagine that the circle is straightening itself out.: Imagine that the circle is straightening itself out.
PowerPoint Presentation: The length of this line segment is the circumference of the circle. 314 cm
The circumference is the same length as 3 diameters plus .14 of another diameter.: The circumference is the same length as 3 diameters plus .14 of another diameter.
So, circumference = diameter x 3.14: So, circumference = diameter x 3.14
Does this look familiar?: Does this look familiar?
O.K., now it’s time to move forward with some new stuff.: O.K., now it’s time to move forward with some new stuff.
How in the world would you find the area of a circle?: How in the world would you find the area of a circle?
Remember, area is always measured in square units.: Remember, area is always measured in square units.
Remember that the area of a rectangle is length x width because you’re calculating the total number of squares inside of the rectangle. : Remember that the area of a rectangle is length x width because you’re calculating the total number of squares inside of the rectangle. 2 4
That’s fine and dandy, but a circle is not a polygon. It does not have straight sides; it has curves.: That’s fine and dandy, but a circle is not a polygon. It does not have straight sides; it has curves.
How are we going to get around these curves?: How are we going to get around these curves?
Imagine chopping up the circle as if it were a pizza.: Imagine chopping up the circle as if it were a pizza.
Now, let’s rearrange our “pizza” into another shape. : Now, let’s rearrange our “pizza” into another shape.
PowerPoint Presentation: PRESTO!
Great Mr. Dunlap! But what in the world is this?: Great Mr. Dunlap! But what in the world is this?
Believe it or not, this is really our “friend” the parallelogram. And, we know how to calculate the area of a parallelogram.: Believe it or not, this is really our “friend” the parallelogram. And, we know how to calculate the area of a parallelogram.
Rats! He always has an answer for everything.: Rats! He always has an answer for everything.
Area = Base x Height: Area = Base x Height Base Height
To find the area of the circle (which is now a parallelogram), we just need to multiply the Base by the Height.: To find the area of the circle (which is now a parallelogram), we just need to multiply the Base by the Height. Base Height
Wait a minute! The height of this “parallelogram” is really the radius of the circle.: Base Radius Wait a minute! The height of this “parallelogram” is really the radius of the circle.
PowerPoint Presentation: 1/2 of Circumference Radius Wait a minute! The Base is really 1/2 of the circumference.
PowerPoint Presentation: 1/2 of Diameter x Radius Wait a minute! The circumference is really Diameter x
PowerPoint Presentation: Radius x Radius Wait a minute! 1/2 of a Diameter is really a Radius.
PowerPoint Presentation: Base Height So if we multiply the Base x Height
PowerPoint Presentation: We are really multiplying Radius x Radius x Radius x Radius
PowerPoint Presentation: Practice Time!
1) Now let’s try this formula. Find the area of this circle.: 1) Now let’s try this formula. Find the area of this circle. 5 cm
5 x 5 x 3.14 = 78.5 square cm: 5 x 5 x 3.14 = 78.5 square cm 5 cm
2) Find the area of this circle.: 2) Find the area of this circle. 6 cm
6 x 6 x 3.14 = 113.04 square cm: 6 x 6 x 3.14 = 113.04 square cm 6 cm
3) Find the area of this circle.: 3) Find the area of this circle. 9 cm
9 x 9 x 3.14 = 254.34 square cm: 9 x 9 x 3.14 = 254.34 square cm 9 cm
PowerPoint Presentation: 4) Find the area of this circle. 20 cm
PowerPoint Presentation: 10 x 10 x 3.14 = 314 cm 2 20 cm Make sure that you use the radius of the circle.
PowerPoint Presentation: 5) Find the area of this circle. 14 cm
PowerPoint Presentation: 7 x 7 x 3.14 = 153.86 cm 2 14 cm Make sure that you use the radius of the circle.
PowerPoint Presentation: 6) Find the area of this circle. 22 cm
PowerPoint Presentation: 11 x 11 x 3.14 = 379.94 cm 2 22 cm
PowerPoint Presentation: Area = Radius x Radius x It’s as easy as pi.