Circumference and Area of a Circle

Circumference and Area of a Circle

Learning Objectives

• Today, we will determine how to find the circumference and area of a circle

• identify the radius and diameter of a circle

What is Circumference?

• C= the distance around a circle

• Formulas for circumference: 

   $C=\pi d$  and  $C=2\pi r$  

• Diameter= double the radius

• Radius= half the diameter

•  $\pi\ \approx3.14$  

Multiple Choice

True or False: The diameter is being pictured here.

• True

• False

Multiple Choice

True or False: The diameter is twice as long as the radius.

• True

• False

Multiple Choice

The diameter of a circle is 10 inches. What is the radius?

• 10 inces

• 20 inches

• 5 inches

• 2.5 inches

Open Ended

The radius of a circle is 12 cm. What is the diameter?

How do I find the circumference using the formula?

1. Determine if you are given the radius or the diameter.
2. Choose your formula. If you are given the diameter, then use 

 $C=\pi d$  If you are given the radius, use  $C=\ 2\pi r$  
3. Plug in what you know. Use 3.14 for pi. 
4. Multiply. 
Sometimes, you will be asked to leave your answers in terms of pi. So, leave the pi symbol in your answer and multiply everything else. 

Example 1: The diameter of a circle is 12 cm. What is the circumference?

 $C=\pi d$  

Plug 12 in for d. Use 3.14 for pi.

c= 3.14(12)
C= 37.68 cm

Example 2: The radius of a circle is 5 inches. What is the circumference?

 $C=\ 2\pi r$  Leave your answer in terms of pi. 

Plug in 5 for r.
C= 2 $\pi$  (5)
Combine like terms
C= 10 $\pi$  
That's it!

Multiple Choice

Find the circumference. Leave your answer in terms of pi. 

 

• 8 $\pi$  

• 4

• 2 $\pi$  

• 4 $\pi$  

Open Ended

Find the circumference of a circle if the radius is 2.5 inches. Use 3.14 for pi.

Area of a Circle

• the amount of space a 2D shape takes up

• measured in square units  $\left(units^2\right)$  

Example 1: Find the area of a circle if the radius is 8 cm. Leave your answer in terms of pi. 

• Remember the formula:

   $A=\pi r^2$  

• Plug in what you know

•   $A=\pi\left(8\right)^2$  

•  $A=\ 64\pi$   $cm^2$  

Example 2: Find the area of a circle if the diameter is 12 inches. Use 3.14 for pi. 

• Remember your formula:

   $A=\pi r^2$  

• Notice: You are given the diameter. But, the formula uses the radius. So, you must divide the diameter by 2, to find the radius. 12/2= 6 inches.

• Now, plug in what you know. 

•  $A=3.14\left(6\right)^2$  

•  $A=3.14\left(36\right)$  

• A=113.04  $in^2$  

Multiple Choice

Find the area of this circle. Leave your answers in terms of pi. 

• $25\pi$

  
  

• $5\pi$

• $10\pi$

• $100\pi$

Multiple Choice

What is the area of this circle? Use 3.14 for pi. 

• 12.56

• 25.12

• 50.24 

• 200.96

Open Ended

Find the area of a circle if the radius is 7 inches. Use 3.14 for pi.