Circumference and Area of Circles

Circumference and Area

Intro to Arc Length and Area of Sectors in Circles

In class, we have been finding arc measures (in degrees). Soon, we will switch gears and find arc length (in ft, cm, in, etc.).

​

Read through the chart to identify differences between arc measure and arc length.​

​

Arc Length vs. Arc Measure

Open Ended

In your own words, describe the difference between arc measure and arc length. (Use the chart on the previous slide for help!)

Multiple Choice

What is the MEASURE of Arc PQ?

• 60 degrees

• 3.82 meters

Multiple Choice

What is the LENGTH of Arc PQ?

• 60 degrees

• 3.82 meters

Multiple Choice

What is the approximate value of pi?

• 3.13

• 3.67

• 3.24

• 3.14

Multiple Choice

True or False: Pi is the ratio of the circumference to the diameter.

• True

• False

To find arc length, we will need to know the circumference of a circle.

​

Circumference: the distance around a circle.​

Circumference

​C = πd

​

d: diameter

π​ ≈ 3.14

​​Using the Diameter

​

C = 2πr

​

r: radius

π​ ≈ 3.14

Using the Radius

​

Multiple Choice

Find the circumference of the circle in the image.

• 10π

• 20π

• 100π

• 20

Multiple Choice

What is the circumference of the circle in the image?

• 6

• 6π

• 12π

• 36π

Multiple Choice

A cruise ship has a large, circular window. It has a diameter of 6 meters. What is the window's approximate circumference?

• 3 m 
• 9.42 m
• 12 m
• 18.84 m

Multiple Choice

Find the circumference of a circle with a radius of 13.5 mm.

• 37.68mm
• 18.84mm
• 84.78 mm
• none of the above

​A sector is a section of a circle bounded by 2 radii and an arc. We will soon find the area of a sector of a circle. To do this, we will need the area of the circle.

​​Sector of a Circle

​

​A = πr²

​

r: radius

π ≈ 3.14​

​

​

​​Area of Circle

Multiple Choice

What is the area of the circle in the image?

• 10

• 20π

• 100

• 100π

Multiple Choice

What is the area of the circle in the image?

• 9π

• 12π

• 12

• 36π

Multiple Choice

Find the approximate area of the circle in the image.

• 63.585 square inches

• 81 square inches

• 20.25 square inches

• 254.34 square inches

Multiple Choice

A circular pin has a diameter of 6.2 centimeters. What is the area of the circle?

• 38.44π square cm

• 9.61 square cm

• 6.2π square cm

• 9.61π square cm

Multiple Choice

A circle has an area of 36π. What is the circumference of the circle?

• 18π

• 12π

• 6π

• 36π