Exploring Areas of Circles, Sectors, and Segments

This video tutorial covers the calculation of areas for circles, sectors, and segments. It begins with a review of the formula for the area of a circle, pi times the square of the radius. The tutorial then explains how to find the area of a sector, which is a fractional part of the circle's area determined by the arc's measure. Finally, it discusses calculating the area of a segment, which involves subtracting the area of a triangle from the sector's area. The video provides formulas and methods for both right and equilateral triangles.

What is the formula to calculate the area of a circle?

• radius^2 / Pi

• 2 * Pi * radius

• Pi * radius^2

• Pi * radius

Tags

CCSS.7.G.B.4

What does the radius of a circle connect?

• None of the above

• Any two points on the circumference

• Center to the center

• Center to any point on the circumference

What geometric shape is used to describe a sector of a circle?

• Square

• Slice of pizza

• Triangle

• Rectangle

Tags

CCSS.1.G.A.1

CCSS.2.G.A.1

How is the area of a sector calculated?

• 2 * Area of circle * (arc measure / 360)

• Area of circle / (arc measure / 360)

• Area of circle * (360 / arc measure)

• Area of circle * (arc measure / 360)

Tags

CCSS.HSG.C.B.5

What is the relationship between the area of a sector and the area of a circle?

• Area of sector is a fraction of the area of the circle

• Area of sector is the same as the area of the circle

• Area of sector is double the area of the circle

• Area of sector is half of the area of the circle

Tags

CCSS.HSG.C.B.5

How is the area of a sector related to the measure of its arc?

• Directly proportional

• Inversely proportional

• Not related

• Equal to the square of the arc measure

Tags

CCSS.HSG.C.B.5

What is the formula to find the area of a sector when you know the arc's degree measure?

• Area of circle * (degree measure / 360)

• Area of circle / (degree measure / 360)

• Area of circle * (360 / degree measure)

• Area of circle + (degree measure / 360)

Tags

CCSS.HSG.C.B.5

What is a segment in a circle?

• Region outside the circle

• Region bounded by two radii

• Region bounded by a chord and an arc

• Full area of the circle

How do you find the area of a circle segment?

• Multiply area of triangle by area of sector

• Divide area of sector by area of triangle

• Add area of triangle to area of sector

• Subtract area of triangle from area of sector

Tags

CCSS.HSG.C.B.5

What type of triangle might you subtract from a sector to find the area of a segment?

• Equilateral

• Right

• Isosceles

• Both Right and Equilateral