The area and circumference of a circle

The area and circumference of a circle

​Learning Objectives

​After studying this topic, students are able to:

​• Know the definition of a circle and the names of its part

• Know and use formulae for the circumference and area of circle

​A. Parts of a circle

Terms:​

​circle: a closed shape formed by tracing a point that moves in a plane such that its distance from a given point (center) is constant.

radius: a line segment from the center to the circumference of a circle or sphere.

​chord: a line segment whose endpoints both lie on a circular arc. diameter is the longest chord in a circle

​diameter: any line segment that passes through the center of the circle and whose endpoints lie on the circle

​tangent: a line which touches the circle at only one point

​secant: a line that intersects a circle at two distinct points

​B. Circumference and area of a circle

Circumference: the distance around the outside of the circle. It is like the perimeter of other shapes like squares.

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​Example 1

​Example 2

​Example 3

​Example 4

​Example 5

​Example 6

Multiple Select

Which segment is the chord?

(select that apply)

• AC

• BD

• LM

• CE

Multiple Choice

What is true about this circle?

• Radius is : DC
• Diameter is: BA
• Radius is :DE
• Diameter is: DC

Multiple Choice

What is circumference?

• The distance around a circle.
• The space inside the circle.
• A line from side to side passing through the center.
• A line from the center to the side.

Multiple Choice

The circumference is 62.8 inches.  What is the radius?

• 20 inches
• 10 inches
• 6.28 inches
• 31.4 inches

Multiple Choice

what is the area of this semicircle ?

• 41.448 cm²

• 82.896 cm²

• 547.114.147 cm²

• 273.557 cm²

Multiple Choice

what is the perimeter of this semicircle ?

• 54.648 cm

• 82.896 cm

• 96.096 cm

• 67.848 cm

Multiple Choice

What is the area of this circle? (in ft²)

• 1384.74

• 2142.12
• 5541.77
• 1289.12

Multiple Choice

Ms. Catall is using a compass to find her way out of the woods. The compass has a radius of 4 centimeters. What is the compass's area?

• 49.2 cm²
• 45.6 cm²
• 50.24 cm²
• 55.9 cm²

Multiple Choice

What is the area of this circle?

• 82.13 m²

• 78.5 m²

• 314.16 m²

• 170.12 m²

Multiple Choice

What is the circumference of a circle with a diameter of 11 millimeters?

• 34.6 mm
• 30 mm
• 25.3 mm
• 34.54 mm

Open Ended

Any questions?