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# Investigating Circles - PowerPoint PPT Presentation

Investigating Circles. Properties of Circles. radius. diameter. Circle A closed curved with all points the same distance from center. •. . origin. area. circumference. Origin. The origin is the center of the circle.

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Presentation Transcript

diameter

Circle

A closed curved

with all points

the same

distance from

center

origin

area

circumference

• The origin is the center of the circle.

• All points on a circle are the same distance from the origin.

• A circle is named by its center.

• Name: Circle A

origin

A

• The diameter is the distance of a line segment going across a circle through its center. AB

• It divides the circle exactly in half.

• Is viewed as a line of symmetry.

• Symbol islower case d.

diameter

• Radius is the distance from the center of the circle to any point on the circle.

• Radius is one-half the length of the diameter.

• Symbol is lower case r.

• Circumference refers to the total distance around the outside of a circle.

• Can also be called the perimeter of a circle.

• Symbol is an upper case C.

• You can estimate the age of a tree by measuring the circumference of a tree. For many kinds of trees, each 2 cm represents one year of growth.

100 cm

• An odometer is an instrument used to measure the distance a vehicle travels by counting the number of wheel revolutions.

• closed curved

• all points same distance from centre (origin)

• diameter

• circumference

• area

• pi

Diameter

Circumference

Ratio of C & d

center of a circle

distance across center of circle (d)

half the distance of diameter (r)

distance around the outside of a circle ( C )

Circumference is actually 3.14 ( )

bigger than the diameter or about 3 times bigger

Concepts you Should Now Know

• If you measure the distance around a circle (C) and divide it by the distance across the circle through its center (d), you should always come close to a particular value

• We use the Greek letter to represent this value.

 (pi)

• The value of  is approximately 3.14159265358979323. . .

• So, C/d always = ___

• Using is a quicker way to find the circumference of a circle.

• Using  allow us to calculate circumference with less measuring,

 (pi)

How  Helps

2cm

• Knowing the value of ,allows us to use formulas to calculate circumference.

• If the diameter of a circle is 2 cm, how could you calculate the circumference?

• C =  x ___

• Estimate the circumference

• The circumference is ____

• C = x d

• C = 3.14 x 3

• C = 9.42cm

If the

diameter is 3cm

Estimate

Is . . .

• C = x d

• C = 3.14 x 1.5

• C = 4.71cm

If the

diameter is 1.5cm

C =  x d

…but we don’t know the diameter

• C = x d

• d = 2 x r

• d = 2 x 3

• d = 6

• C = 3.14 x 6

• C = 18.84m

If the

• C = x d

• C = 3.14 x 5

• C = 15.7

Estimate is . .

If the

diameter is 5

What formula could I use?

What is the diameter of a circle if the

circumference

is 18.8?

What is the diameter of a circle if the

circumference

is 13.2?

What is the diameter of a circle if the

circumference

is 33.9?

Estimate the area of this circle.

Seeing the square units can help.

Remember each block is one square unit

Estimate is

Counting square units can give you a good estimate, however, can be time consuming.

Counting will not always give an exact answer.

Actual is

The formula for finding the area of a circle is

A =  x r x r

or  r2

Estimate is

Estimated area is

Remember

A =  x r x r

or  r2

Actual area is

Estimated area is

Actual area is

• To cut across a circular park has a you would travel 0.8 of a kilometer. How far would you travel around the park?

• A spoke of a bicycle wheel is 12 cm. What will be the distance of one turn of the wheel?

FOIL

(2x – 5)(3x +6)

First

Outside

Inside

Last

Collect Like Terms

(2x – 6)(x + 7)

Other SkillsFactoring

2x² + 14x + 12

Find a. b. c.

Multiply a x c

Find two numbers