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Circumference and Area of Circles
Know how to solve the following:


 Find the AREA and CIRCUMFERENCE of circles with the following:

1 - 3  Use 3.14 for pi.  (A= (pi)r2; C = d(pi); C = 2(pi)r)
A= (pi)(r)(r)or
A = (pi)(radius squared)
1.  radius  = 5
2.  diameter = 8
 3. r = 3.1
Area = 3.14(5)(5)
A = 3.14(25)
A= 78.5 square units

radius = 8/2 or 4
A = 3.14(4)(4)
A = 50.24 units squared


 A= 3.14(3.1)(3.1)
A= 30.18 square units
(which is the same as 30.18 units squared)
C= (pi)d or
C = (pi)(2)(r)

1.  radius  = 5
2.  diameter = 8
 3. r = 3.1
d = 2r or 2(5) = 10
10(3.14)
C = 31.4 units
C = 8(3.14)
C= 25.12  units
d = 3.1(2) or 6.2
C = 6.2(3.14)
C = 19.27 units
  4 - 6 Use 22/7 for pi.                  
4.  radius = 7
 5.  radius =  11
6.  diameter = 3/28
(radius = 3/ 56)
A = 22/7 (7)(7)
A = 22/7 (49)
A = 22(7)
A = 54square units

C = 22/7(14)
You finish this.
 A = 22/7 (11)(11)
A = 22/7 ( 121)
A = 2662/7
A = 380.29 square units

C = 22/7 (22)
A = 22/7 (3/56)(3/56)
A = 22/7 ( 9/3136)
A = 198/21952
A = 99/10976 square units

C = 22/7 ( 3/28)
7 - 9     Use the calculator for pi.

7.     diameter = 3          8.  radius = 8               9. diameter = 3/4

Look at the examples above and try these on your own.  There is a calculator on your computer.


10.  Find the radius of a circle whose Circumference = 30 units
 C= pr(2)
30 = 2pr
30/2 = 2/2 pr
15 = pr
15/p = pr/p
15/3.14 = r
4.78 = r

11.  Find the diameter of a circle whose Area = 113.04 square units.
                 2
A = pr                                 substitute known values
                                      2             
113.04 =3.14r                   divide both sides by 3.14
                                         2
113.04/3.14 = r                  simplify
                 2
36 = r                                    find the square root of each side of the equation
6 = r

12. Find the area of the shaded sections of the figures below.
 
Notice that the two circles span the rectangle so that the circumference touches the rectangle on all sides.  Therefore, we can use the number of circles to find the length of the rectangle in units.  The sum of the diameters of the circles equal the length of the rectangle.  

Therefore the rectangle has an area of 1(2) or 2 units squared.  A = lw

The radius of the circles is 1/2 the diameter or 1/2.  There are two circles so the area would have to include both. The area of the circles would be

                         2
A = (2) pr
A = (2) (1/2) (1/2) p
A = 1/2p

Using 22/7 for p would be a good idea here because 22/7 (1/2) = 11/7.
Subtract the area of the circles from the area of the rectangle.
2 - 11/7 = 14/7 - 11/7 or 3/7.
.



                                         2
14.                                6









15 - 17 You are planning a pizza party.  You are having 8 guests.  
15.  If an 8-inch pizza feeds 2 people and cost $9.00 and a 12-inch pizza costs $15, how many people will the 12 inch pizza feed.  

16.  How many pizzas would you need to buy for the party.

17.  What size pizzas would give you the best buy?




18 - 20 Write an explanation of why race car drivers have an advantage if they drive on the inside of a circular track. Are there any disadvantages?  Explain.
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