Circumference and Area of a Circle

Circumference and Area of a Circle

Circle

The set of points equidistant from a given point called the center

Parts of a Circle

Circumference - the distance around the circle

Diameter - the distance across the circle, through the center

Radius - The distance from the center to any point on the circle

Multiple Choice

What does the red line represent?

• The circumference of the circle

• The diameter of the circle

• The radius of the circle

Radius and Diameter

The diameter is twice as long as the radius.

d = 2r

The radius is half the length of the diameter.

r = d/2

Multiple Choice

The diameter of a circle is 10 in.

What is its radius?

• 20 in.

• 5 in.

Pi

The ratio of a circle's circumference to its diameter.

Used to calculate the circumference and area of a circle.

Multiple Choice

Which ratio is used to calculate Pi?

• C/r

• C/d

• r/C

• d/C

Solve for C

 $\pi$  =  $\frac{C}{d}$  
 $\pi$   $\times$  d =  $\frac{C}{d}$   $\times$  d
 $\pi$  d = C
C =  $\pi$  d

Circumference

Formulas:

C =  $\pi$  d

C = 2  $\pi$  r 

Solve a Circumference Problem

1. Write the formula

2. Substitute the values

3. Multiply

4. Write the unit of measure

Multiple Choice

Calculate the circumference of the circle.
C =  $\pi$  d

• 98.91 ft.

• 63 ft.

• 197.82 ft.

Given a circle with a diameter of 63 ft.

calculate the circumference

• C =  $\pi$  d

• C = 3.14 x 63

• C = 197.82 ft.

Area of a Circle

A =  $\pi$   $r^2$  

A =  $\pi$   $\times$  r  $\times$  r

Solve an Area of a Circle Problem

1. Write the formula
2. Substitute the values
3. Simplify
4. Write the unit of measure  $units^2$  

Multiple Choice

Does this circle show the radius or diameter?

• radius

• diameter

Multiple Choice

According to the Area of a Circle formula, do you need to know the radius or diameter?
A =  $\pi$   $r^2$  

• radius

• diameter

Multiple Choice

What is the radius of this circle?

• 40 cm

• 20 cm

• 10 cm

Multiple Choice

Calculate the Area of the circle.

A =  $\pi$   $r^2$  

• 314  $cm^2$ 

• 62.8  $cm^2$  

• 1256  $cm^2$  

Given a circle with a diameter of 20 cm.

calculate the area.

• Since d = 20, r = 10

• A =  $\pi$   $r^2$  

• A = 3.14 x 10 x 10

• A = 314  $cm^2$