Circles

A circle is a shape with all points the same distance from its center. The distance around a circle is called its c

ircumference

. The distance across a circle through its center is called its

diameter

.

 (pi) is the ratio of the circumference of a circle to its diameter. For any circle, if you divide its circumference by its diameter, you get a value close to 3.14159. This following formula: C/D = where C is the circumference and D is the diameter.

The

radius

of a circle is the distance from the center of a circle to a point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. So a circle's diameter is twice as long as its radius.

The formula for the circumference of a circle is given by either :

C

 

d

or

C

 2

πr

Example : The diameter of a circle is 3 cm. What is its 

= 3.14

) Solution:  C = 3.14 · (3 cm) C = 9.42 cm 3 cm

Example : The radius of a circle is 2 in. What is its circumference? (Use

= 3.14

)

C

 2 

r C

 2  3 .

14  2

C

 12 .

56

in

Example : The circumference of a circle is 15.7 cm. What is its diameter? (Use

= 3.14

) • 15.7 cm = 3.14 · d d = 15.7 cm

÷

3.14

d = 5 cm

The area of a circle is the number of square units inside that circle. If each square in the circle below has an area of 1 sq.cm, you could count the total number of squares to get the area of this circle. If there were a total of 28.26 squares, the area of this circle would be 28.26 csq.m

The area of a circle is given by the formula

A

 

r

2

Example : The radius of a circle is 3 in. What is its area?

 (Use

= 3.14

) • Solution:

A = · r · r

• A = 3.14 · (3 in) · (3 in) • A = 3.14 · (9 sq.in) • A = 28.26 sq.in

Example: The diameter of a circle is 8 cm. What is its area?

(Use

= 3.14

) • •

r

= 4 cm • A = 3.14 · (4 cm) · (4 cm) • A = 50.24 sq.cm

Example: The area of a circle is 78.5 sq.m. What is its radius? (Use

= 3.14

) 

r

2 • Solution:

A =

• 78.5 sq.m = 3.14 ·

r

2 • 78.5 sq.m ÷ 3.14 =

r

2 • 25 sq.m =

r

2 • r = 5 m 

r

2

Find the area of the rectangular piece of metal after the 2 circles are removed.

16 cm 10.00 cm 28.00 cm 45.00 cm

Find the perimeter and area of the shape.

P P P

   39 .

2  79 5  39 .

5  3 .

1  2  14

C



C

 39 .

26 .

0  5  1 2

C P

 79  81 .

64

P

 160 .

64

in A



A



A rect

39 .

5  

A circle

26 .

0   3 .

14  13 .

0  2

A

 1027  530 .

66

A

 1557 .

66

in

2

A belt connecting two 9-in-diameter drums on a conveyor system needs replacing. How many in long must the belt be if the centers of the drums are 10 ft apart? Round to tenths.

9 in 9 in 10 ft