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Investigating Circles - PowerPoint PPT Presentation


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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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radius

diameter

Circle

A closed curved

with all points

the same

distance from

center

origin

area

circumference


Origin
Origin

  • 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


Diameter
Diameter

  • 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
Radius

  • 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
Circumference

  • 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.




Making connections
Making Connections

  • 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


Making connections1
Making Connections

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


Circle properties
Circle Properties

  • closed curved

  • all points same distance from centre (origin)

  • radius

  • diameter

  • circumference

  • area

  • pi


Concepts you should now know

Origin

Diameter

Radius

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



Ratio of the circumference of a circle to its diameter
Ratio Of The Circumference Of A Circle To Its Diameter

  • 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)


Ratio of the circumference of a circle to its diameter1
Ratio Of The Circumference Of A Circle To Its Diameter

  • 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
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 ____


Circumference of a circle
Circumference of a Circle

  • C = x d

  • C = 3.14 x 3

  • C = 9.42cm

If the

diameter is 3cm


Circumference of a circle1
Circumference of a Circle

Estimate

Is . . .

  • C = x d

  • C = 3.14 x 1.5

  • C = 4.71cm

If the

diameter is 1.5cm


Circumference of a circle2
Circumference of a Circle

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

radius is 3m


Circumference of a circle3
Circumference of a Circle

  • C = x d

  • C = 3.14 x 5

  • C = 15.7

Estimate is . .

If the

diameter is 5


Diameter of a circle
Diameter of a Circle

What formula could I use?

What is the diameter of a circle if the

circumference

is 18.8?


Diameter of a circle1
Diameter of a Circle

What is the diameter of a circle if the

circumference

is 13.2?


Diameter of a circle2
Diameter of a Circle

What is the diameter of a circle if the

circumference

is 33.9?



Area of a Circle

Estimate the area of this circle.


Area of a Circle

Seeing the square units can help.

Remember each block is one square unit

Estimate is


Area of a Circle

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


Area of a Circle

Estimated area is

Remember

A =  x r x r

or  r2

Actual area is


Area of a Circle

Estimated area is

Actual area is


Choosing a formula
Choosing a Formula

  • 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?


Other skills
Other skills

FOIL

(2x – 5)(3x +6)

First

Outside

Inside

Last

Collect Like Terms


Multiplying binomials
Multiplying Binomials

(2x – 6)(x + 7)


Other skills factoring
Other SkillsFactoring

2x² + 14x + 12

Find a. b. c.

Multiply a x c

Find two numbers

that add to b

( )( )

x in each

Divide by a

Kickback


Factoring
Factoring

3x² + 12x + 12


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