Area of Sector Discovery

Presentation

•

Mathematics

•

9th Grade

•

Practice Problem

•

Medium

•

CCSS

HSG.C.B.5, 7.G.B.4, HSF.TF.A.1

Standards-aligned

Diana Guerrero

Used 1+ times

FREE Resource

5 Slides • 10 Questions

Area of Sectors

How do you find the area of a sector of a circle?

What is a SECTOR?

A sector of a circle is a region bounded by two radii and their intercepted arc.

A sector is named by the endpoints of the arc and the center of the circle. For example, the figure shows sector POQ.

Let's derive the formula for the area of a sector

The following questions will walk you through "discovering" the formula for finding the area of a sector in a circle.

Multiple Choice

Which of the following is the formula for finding area of a circle?

$A=\pi r^2$

$A=3r^2$

$A=0.5\pi r^2$

$A=2\pi r$

Dropdown

First, find the area of the circle.

A=\pi r^2

= π(

)²

A ≈

Dropdown

The area of sector AOB is

\frac{1}{3}

of the circle's area.

Area of sector AOB =

\frac{1}{3}

∙

mm²

Open Ended

How could you use the above process to find the area of a sector of the circle whose central angle

measures m°?

Type response here

Multiple Choice

What do you think is the formula for the area of a sector with a central angle of x° and radius r?

$\frac{x\cdot2\pi r}{180}$

$\frac{x\cdot\pi r^2}{360}$

$\frac{x\cdot2\pi r}{360}$

$\frac{x\cdot\pi r^2}{180}$

Area of a Sector

Labelling

Find the area of the sector, round the nearest hundredth.

$A=\frac{x\degree\cdot\pi r^2}{360}$

Drag labels to their correct position on the image

210

48.47

150

0.58

16.49

360

Labelling

Find the area of the sector, round the nearest hundredth.

Drag labels to their correct position on the image

287.77

47.96

144

164.62

229

360

27.43

131

Open Ended

Your friend said that the value of x° in the formula for the area of a sector can never be larger than 360°. Do you agree or disagree? Explain your reasoning.

Type response here

Math Response

Find the area of the sector, round to the nearest hundredth.

Type answer here

Deg^°

Rad

Math Response

Find the area of the sector, round to the nearest hundredth.

Type answer here

Deg^°

Rad

Area of Sectors

How do you find the area of a sector of a circle?

Show answer

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Area of Sector Discovery

Area of Sectors

Let's derive the formula for the area of a sector

​Area of a Sector

Area of Sectors

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Area of a Sector