8-1C The Circumference of a Circle

What is circumference?

What is pi?

What is the symbol for pi?

What are the formulas for the circumference of a circle?

Circumference

• Circumference is the distance around a circle.

• Perimeter is to a rectangle as circumference is to a circle.

Measure up• Measure the circumference and diameter

of three circular objects.

• Calculate the ratio of the circumference to the diameter to the nearest tenth.

object circumference diameter ratio

Mug

Tube

Cylinder

Circumference to diameter ratio

• The ratio of the circumference to the diameter of a circle is the number pi (π).

• Pi is an irrational number. Its’ decimal representation does not terminate or follow a repeating pattern.

• We use 3.14 as the value for π.

• Find the π button on your calculator.

Definition

The number π is the ratio of the circumference of any circle to its diameter.

d

c

Theorems

• The circumference of a circle is the product of π and its diameter d.

C = πdThe circumference of a circle is twice

the product of π and its radius r

C = 2πr

Exact or Approximate?

• Answers from problems with π in them can be written two ways.

• Exact answers leave the π symbol as part of the answer.

• Approximate answers use the decimal approximation (3.14…) and the answer is in decimal form.

If the radius of ּסC is 4 cm, what is the circumference to the nearest tenth?

C = 2πr C = πdWhich formula should you use?

Which formula has the variables you are given in the problem?

C = 2π(4)

= 8π (exact answer)

≈ 25.1 cm (approximate answer)

What is the circumference of the pan? Round your answer to the nearest tenth.

C = π(8)

= 8π (exact)

≈ 25.1 in (approximate)8 in

C = πd C = 2πr? ?? ?

The circumference of a trash can lid is 22π. What is its diameter?

What formula do you use?C = πd

The 22π replaces what letter?C

What variable do you solve for?d

22π = πd (divide both sides by π)d = 22

• What is circumference?

Circumference is the distance around a circle.

• What is pi?

The ratio of the circumference to the diameter of a circle.

• What is the symbol for pi?

π

• What are the formulas for the circumference of a circle?

C = 2πr C = πd

Assignment 8-1CPage 553, 1-8, 20-26No formulas with numbers

No credit