Circles

1
Circles

• How to find the area of a circle and the parts of
  a circle.

2
What is a circle?

• A circle is a shape with all points the exact
  same distance from its center.
• A circle is named by its center. For example, the
  circle below would be circle A.

3
What is Area?

• Area is the amount of space that an object takes
  up. You can also think of it as the amount of
  space inside the object.
• When finding the area of a circle you are really
  trying to find out how much space is inside of
  the circle.
• Area is measured in units squared.
• For example sq. cm (square centimeters)
• sq. ft (square feet)

4
Parts of a Circle

• There are two parts of circle that we will be
  concerned with radius and diameter.
• The radius of a circle is the distance from the
  center of the circle to any point on the circle.
  It is also half of the diameter.
• The diameter is a line that runs from one side of
  the circle to the other through the center. This
  line cuts the circle in half.

5
What is PI?

• PI is a number that we need to use to find the
  area of a circle. This number is derived
  mathematically and can be computed to many
  decimal places. For our use, however, we will use
  PI3.14
• The sign used to represent pi looks like this TT

6
The Formula

• The formula to find the area of a circle is
• A TT R R orA TT R2In this formula
• AArea
• RRadius
• TT3.14

7
Finding the Area

• So where do you get all of these numbers from?
• Pi (TT) is always equal to 3.14. It is a
  constant.
• If the radius is given in the problem, use that
  number.
• If the radius is not given but the diameter is,
  you need to use this number to find the radius.
• To do this remember that the radius is one
  half of the diameter. Therefore, r1/2d or rd/2

8
Why Would You Need To Know the Area of a Circle?

• Lets look at an example.
• Brian wants to put a circular spa (hot tub) in
  his deck. He knows that the diameter of the hot
  tub is 4 feet. How big of a hole does he need to
  cut in his deck to fit in the hot tub? (In other
  words, what is the area of the hot tub?)

9
Finding the Area

• Lets find the area of Brians hot tub.
• We know that the diameter is 4 feet, but we need
  to know the radius. How do we find this?
  
• Remember, rd/2
• This means that r4/2 or r2
• Also, remember that TT3.14
• Now we can use the formula ATTr2
• A 3.1422
• Now we can solve for this formula.
• A3.144
• A12.56 sq. ft.

10
Where Did the Units Come From?

• We said that Brians hot tub had a diameter of 4
  feet.
• When solving the formula remember that r2 means
  rr.
• This is like saying feetfeet. This will give you
  feet squared or square feet.
• This can be written either sq. ft, or ft2.

11
Links

• Math Goodies
• This page has both information and some drill
  exercises. If you scroll to the bottom of the
  page you can try a few problems. You can even
  have your answers checked!
• Another Worksheet
• Here is another sheet you can try for practice.

12
Worksheet

• Worksheet for Homework
• Answers to the Worksheet