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.

Fill in the Blanks

What did the ratio of the circumference/diameter simplify down to for each type of bike?

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

Fill in the Blanks

A Ferris wheel travels in a circular motion and measures 40 meters from the top car to the bottom car.

What is the radius of the Ferris Wheel? [Number Only]

Fill in the Blanks

A Ferris wheel travels in a circular motion and measures 40 meters from the top car to the bottom car.

What is the diameter of the Ferris Wheel? [Number Only]

Fill in the Blanks

A Ferris wheel travels in a circular motion and measures 40 meters from the top car to the bottom car.

A car travels 1 time around the Ferris wheel. How many meters did the car travel? [Number Only]

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

Fill in the Blanks

A circular rug measures 8 ft across. What is the area of the rug?

Fill in the Blanks

Two different circular fountains are being considered for an outdoor patio. How many more square feet will the larger fountain occupy than the smaller fountain?