Circles ~ Major Lesson

Circumference of a Circle

By Courtney Tout

Circumference - the distance around the circle

​

Diameter - the distance from the edge through the center to another edge

​

Radius - the distance from edge to center

​

Center - the middle most point​

Parts of a Circle​

Multiple Choice

_____________ is the distance around the circle

• circumference

• center

• radius

• diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

Does this picture show the diameter or radius of a circle?

• Diameter

• Radius

Multiple Choice

• Radius

• Diameter

• Center

• Chord

Multiple Choice

What part of a circle does the red line represent?

• the radius

• the diameter

• the circumference

Multiple Choice

What is the length around a circle called?

• the radius

• the diameter

• the circumference

The most commonly used value of pi.​

​​Pi

Use this version of pi when you have radius or diameters that are multiples of 7.

​

Ex: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70​

• The ratio between a circles circumference and its diameter.

​

• ​

Multiple Choice

What is the best description of pi?

• 22/7
• 3.1415926
• the ratio of a circle's circumference to its diameter
• the surface area of a sphere of diameter 22/7

Multiple Choice

Which of these ratios is the closest approximation of pi?

• 13/4

• 16/5

• 19/6

• 22/7

Multiple Choice

The symbol for Pi is

• π
• Σ
• Ψ
• ⊈

Multiple Choice

We use this value for PI:

• 3.14
• 314
• 3.41
• 31.519875

Multiple Choice

Which formula below would you use to find π?

• C/d = π
• C x d= π

Multiple Choice

π is equal to circumference divided by _________________.

• radius
• diameter
• area
• itself

Multiple Choice

The diameter of a circular pool is 24.8 feet and the circumference is 77.9 feet. What should you do to find π?

• 77.9 / 24.8

• 24.8 / 77.9

The relationship between Radius and Diameter is simple.​

Radius Vs Diameter

​Radius is half the size of the diameter, so we can use the following formula to find radius when given diameter:​

​Diameter is 2 times the size of the radius, so we can use the following formula to find diameter when given radius:

Multiple Choice

_____________ is twice the radius

• circumference

• center

• radius

• diameter

Multiple Choice

_____________ is half of the diameter

• circumference

• center

• radius

• diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

What is the diameter?

• 8
• 16
• 10
• 4

Multiple Choice

What is the radius?

• 18
• 72
• 38
• 14

When you are given Radius, use

​

When you are given Diameter, use​

​Some text here about the topic of discussion.

Circumference Formulas​

​Practice filling in the information into the formulas

Multiple Choice

Other than the formula C=πd what is another formula for circumference of a circle?

• C=2π
• C=2πr
• C=πr²
• C=πd²

Multiple Choice

A DVD has a diameter of 15 millimeters. Which equation would help you determine the circumference?

• c = 15π
• C = 2π15
• c = 15 ÷ π
• c = 15 π

Multiple Choice

What is the circumference of a circle with a diameter of 9?

• 81π
• 9π
• 3π
• 6π

Multiple Choice

Set up the formula to find circumference.

• C = 9 $$\pi$$  

  C = 9 x 3.14

• C = 18 $$\pi$$  

  C = 18 x 3.14

• C = 2 x 3 x $$\pi$$  

  C = 2 x 3 x 3.14

• C = 18 x 2 x $$\pi$$  

  C = 18 x 2 x 3.14

Multiple Choice

Set up the formula to find circumference.

• C = 9.9 x π

  C = 9.9 x 3.14

• C = 9.9 x 2

• C = 9.9 x 2 x π

  C = 9.9 x 2 x 3.14

• C = 3.14 x π

  C = 3.14 x 3.14

1. Identify which formula to use - including what Pi to use!

2. Plug in what you know

3. Solve!​

Steps - to - Success​

Step 1: We are given Diameter, so we will use

C = pi x d

​

Step 2: Plug information in

​C = 4 x 3.14

​

Step 3: Solve​

C = 12.56​

​​Example 1

​= 4 x 3.14

= 12.56​

Step 1: We are given radius, so we selected:

C = 2 x pi x r

​

Step 2: Plug in what we know:

C = 2 x 3 x 3.14

​

Step 3: Solve

C = 18.84 Inches​

​​Example 2

​

Multiple Choice

Daniel wants to buy cookies for her friend. The radius of a cookie is 5 inches. What is the cookie’s circumference?

• 10 in
• 2.5 in
• 15.7 in
• 31.4 in 

Multiple Choice

Find the circumference (to the nearest whole number)

• 88 in
• 44 in
• 116 square in
• None of the above

Multiple Choice

Find the Circumference (round to nearest tenth):
diameter = 10 mi

• 31 mi
• 31.4 mi
  31.4 mi
• 31.5 mi
  31.5 mi
• 62.8 mi

​We can use the circumference formula when given radius:

C = 2 x pi x r

To help us discover the formula for Area of a Circle​

​

Deriving Area of a Circle Formula

​Watch as the circle is transformed into a parallelogram and the area of a circle formula is derived.​

Multiple Choice

We are taking our circle and its' slices and transforming it to form into a parallelogram. One slice is how tall?

• The size of the circumference 

• The size of pi 

•  The size of the diameter

• The size of the radius 

Multiple Choice

We are taking our circle and its' slices and transforming it to form into a parallelogram. How long should it be?

• The size of the circumference 

• Half the size of the circumference

• T

• The size of the radius

Multiple Choice

What is the formula for area of a circle?

• $$A=\pi d$$  

• $$A=2\pi r$$  

• $$A=\pi r^2$$  

• $$A=\pi d^2$$  

We have transformed our circle, into a parallelogram and relabeled.

​

​Area of Parallelogram = b x h​

​​base = 1/2 C --> 1/2(2Πr)

height = r

​

1/2 (2​)(Πr) (r) = Π x r x r or Πr²

​Using the Area of a Parallelogram formula, lets' determine the area of the parallelogram.

​Area of Circle = Π x r x r

​Area of Circle = Π x r²

Multiple Choice

What is the formula for area of a circle?

• $$A=\pi d$$  

• $$A=2\pi r$$  

• $$A=\pi r^2$$  

• $$A=\pi d^2$$  

Multiple Select

What all information do you need to know to determine Area of a Circle? [Hint: Select 2 choices]

• Diameter

• Circumference

• Radius

• Pi

Multiple Choice

A circular swimming pool is 21 feet in diameter.

How many square feet is the area of the pool?

• 693 ft²

• 346.5 ft

• 65.94 ft²

• 346.5 ft²

Multiple Choice

Ms. Catall is using a compass to find her way out of the woods. The compass has a radius of 4 centimeters. What is the compass's area?

• 49.2 cm²
• 45.6 cm²
• 50.24 cm²
• 55.9 cm²

Multiple Choice

Find the area of the circle

• 43.96
• 153.86
• 87.82
• 307.72

Multiple Choice

What is the area of this circle?

• 82.13
• 78.54
• 314.16
• 170.12

Multiple Choice

What is the area of this circle?

• 452.39
• 139.12
• 113.1
• 84.23

Multiple Choice

What is the area of this circle?

• 50.27
• 78.23
• 98.12
• 201.06

Multiple Choice

What is the area of this circle?

• 62.59
• 113.1
• 19.81
• 28.27

Multiple Choice

What is the area of this circle?

• 1256.64
• 31.41
• 314.16
• 123.12