8-1D Area of a Circle

1
8-1D Area of a Circle

• What is the formula for the area of a circle?
• What part of a circle is common to both the area
  formula and circumference formula?
• What is an annulus?

2
Area of a Circle

• The formula for area of a circle is
• A pr2
• A area r radius
• Deriving the area formula can be found on pages
  556-557.

3
If the radius of ?C is 3 cm, what is its area?
Answer in exact form.

• A pr2
• A p32
• A 9p

4
If the area of ?C is 49p, what is its diameter?

• A pr2
• 49p pr2
• p p
• 49 r2
• r 7

5
The South Rose window in Notre Dame has a
diameter of 12.9 meters. Find the area and
circumference of the window.
C 2pr C 2p(12.9) C 25.8p C 81.05 meters

• A pr2
• A p(12.9)2
• A 166.41p
• A 522.79 meters2

6
Theorem

• The area of a circle is the product of p and the
  square of its radius r.
• A pr2

7
If the area of ?M is 121 m2, find its
circumference.

• A pr2
• 121 pr2
• p p
• 38.5 r2
• r 6.2 m

C 2pr C 2p(6.2) C 38.99 m
?M
What letter is common to both the area and
circumference formulas?
r (radius)
8
Annulus

• An annulus is the region enclosed by two
  concentric circles.

9
Find the area of the annulus shown.

• Big circle
• A p52
• A 25p
• A 78.54

Small circle A p32 A 9p A 28.27
3
5
Big circle - Small circle 25p-9p 16p 78.54
-28.27 50.27
10

• What is the formula for the area of a circle?
• A pr2
• What part of a circle is common to both the area
  formula and circumference formula?
• r (radius)
• What is an annulus?
• The region enclosed by two concentric circles.

11
Assignment

• Page 558, 1-5, 12, 17-20