6th Grade Math Textbook, Fundamentals

 &KDSWHU

10-8

Key Concept

Circumference of a Circle

Cd, or C 2 r, where dis the diameter of the circle and

ris the radius of the circle

Key Concept

Area of a Circle

Ar^2 , where ris the

radius of the circle

Whenever any value—even the

value supplied by your calculator’s

key—is substituted for in a

formula, the solution will be an

approximation. Use the symbol to

express the approximate solution.

C d r

Find the circumference of a circle with a diameter

of 4.5 miles. Express the solution in terms of . Then

estimate Cto the nearest 0.1 mile.

Cd C4.5miles

Find the estimated circumference using 3.14 for the

approximate value of .

Cd C 4.5(3.14) miles C14.13 miles

The circle’s circumference is 4.5miles or about 14.1 miles.

You can divide a circle into equal sectors and then assemble the

sectors so that they create a shape that looks like a parallelogram.

Notice that the base of the “parallelogram” above is approximately equal

to C, and its height is equal to r. So the area formula for a parallelogram

helps you develop an area formula for a circle.

Abh A( C)r A (2r)r Ar^2

In the formulas for circumference and for area, the constantis .
The variables in these formulas are dand r.

1

2

1

2

1

2

C

r



C  b

r  h

Circumference and Area of a Circle

Objective To use a formula to find the circumference of a circle• To use a formula to find

the area of a circle• To find the radius or diameter of a circle given its circumference or area

The Navy Pier Ferris Wheel in Chicago, Illinois, has a diameter
of 140 feet. The circumference of the wheel is about 440 feet.
What is the ratio of the circumference of the wheel to its diameter?

The distance around a circle is called its. The

circumference of the Ferris wheel is approximately 440 feet.

Because 440  140 3.142857, the circumference of the wheel

is a little more than three times the diameter.

For any circle, the ratio of the circumference to the diameter

is a constant value, , where is the Greek letter pi.

You can multiply both sides of by dto getC  d.

The numberis irrational, with a value of 3.141526..., but

3.14 or is sometimes used as an approximation for .

C

d

C

d

circumference

22

7

Remember:The diameter of a

circle is twice its radius: d 2 r.