circles. a circle is a shape with all points the same distance from its center. the distance around...

Circles

A circle is a shape with all points the same distance from its center.

The distance around a circle is called its circumference.

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

(pi) is the ratio of thecircumference of a circle to its

diameter. For any circle,if you divide its circumference by its

diameter, you get avalue close to 3.14159. This

relationship is expressed in thefollowing 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 :

πr C dC 2or

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

circumference? (Use = 3.14)

Solution: C = dC = 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)

inC

C

rC

56.12

214.32

2

Example : The circumference of a circle is 15.7 cm. What isits diameter? (Use = 3.14)

• C = d

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

2rA

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 = · r · r• 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)

• Solution: A =• 78.5 sq.m = 3.14 ·• 78.5 sq.m ÷ 3.14 =• 25 sq.m =• r = 5 m

2r2r2r

2r

2r

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

removed.

28.00 cm

45.00 cm

10.00 cm16 cm

Find the perimeter and area of the shape.

inP

P

P

CP

CCP

64.160

64.8179

0.2614.379

5.3922

15.39

2

15.39

2

2

66.1557

66.5301027

0.1314.30.265.39

inA

A

A

AAA circlerect

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 in9 in10 ft