Circle (circumference and area)

Circle (circumference and area)

7.G.1, 7.G.4, 7.G.6

Circumference and Parts

Parts of a Circle

• Radius, r: the distance from the center of the circle to the outside edge

• Diameter, d: a straight line that passes through the center of the circle; it has two endpoints on the circle

• Circumference, C: the distance around a circle.

C/D

Micah and his friends work at a tire factory. The factory manufactures several different sized tires for different vehicles. Please simplify the ratio set up for each type of bike.

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Circumference

• The circumference of a circle is the distance around the circle. It can be found using two formulas.

•  $c=\pi d$  

•  $c=2\pi r$  

•  $\pi\ can\ be\ approximated\ to\ 3.14$  

Multiple Select

Which of the following are the correct circumferences for this circle?

•  $12\pi$  

•  $37.68\ in$  

•  $6\pi$  

•  $18.84\ in$  

Multiple Select

Which of the following are the correct circumferences for this circle?

• 43.96 cm

•  $28\pi$  
  

•  $14\pi$  
  

• 87.92 cm

Area

Area of a Circle

• The area of a circle measures the covering of a two-dimensional object.

• Use the formula:

•  $A\ =\ \pi r^2$  

•  $r^2\ =\ r\times r$  

•  $So\ that\ means\ A=\ \pi\times r\times r$  

Example 1 (Use 3.14 for Pi)

• Formula:  $A\ =\ \pi r^2$  

• radius = 3 in

•  $\pi\ =\ 3.14$  

•  $A\ =\ 3.14\left(3^2\right)$  

•  $A\ =\ 3.14\left(9\right)$  

•  $A\ =\ 28.26\ in^2$  

Multiple Choice

Please find the area of this circle with the given dimension.

• $39.25\ cm^2$

• $40\ cm^2$

• $78.5\ cm^2$

• $80cm^2$

Multiple Choice

Please find the area of this circle with the given dimension.

•  $114\ cm^2$ 

•  $113.04\ cm^2$ 

•  $113\ cm^2$ 

•  $114.04\ cm^2$ 

What to do if the area is known but other parts are not.

• Sometimes the area of the circle may be known, but your radius or diameter is not known.

• Using the formula for Area is key to solving for your missing piece of information.

Example 2: A circle has an area of 78.5 in². What is the radius of the circle?

• Known:  $A\ =\ \pi r^2$  

•  $A=78.5in^2$  

•  $\pi\ =\ 3.14$  

•  $78.5\ =\ 3.14r^2$  

•  $\frac{78.5}{3.14}\ =\ \frac{3.14}{3.14}r^2$  

•  $25\ =\ r^2$  

• Square Root to find the answer:  $r\ =\ 5$  

Multiple Choice

A pizza has a diameter of 18 inches. It is then cut into eight equal pieces. About how many square inches is each slice of pizza?

• 15.9

• 31.8

• 47.7

• 35.4

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