Arc Lengths and Areas of Sectors

Slides:

Advertisements

Similar presentations

Area of a Sector and Arc Length Geometry BowerPower.net Mr. Bower.

Advertisements

Introduction A sector is the portion of a circle bounded by two radii and their intercepted arc. Previously, we thought of arc length as a fraction of.

Deriving the Formula for the Area of a Sector

7.7: Areas of Circles and Sectors

Circle Properties An Arc is a fraction of the circumference A sector is a fraction of a circle. Two radii and an arc A B O 3 cm r = 3 cm d = 6 cm Arc AB.

Distance around the circle 2  r = C or d  = C.

11.6 Arc Lengths and Areas of Sectors

CIRCUMFERENCE: or If you unwrap a circle, how long will the line be?

7-6 Circles & Arcs 7-7 Area of Circles and Sectors.

TODAY IN GEOMETRY…  Review: Arc Length  Learning Target : 11.5 You will find area of circles and sectors  Independent practice.

TODAY IN GEOMETRY…  Review: Arc Length  Learning Target : 11.5 You will find area of circles and sectors  Independent practice.

Finding the radius or ѳ. Steps to find the radius or ѳ Bring 360 up and multiply Bring 360 up and multiply Multiply what you can on the right Multiply.

Vocabulary: SECTOR of a circle: a region bounded by an arc of the circle and the two radii to the arc’s endpoints SEGMENT of a circle: a part of a circle.

Warm up for Section 4.8.

Lesson 8-2: Formulas 1 Lesson 8-2 Formulas Circumference Arc Length Area Sector.

Basic Terminology Central Angle: An angle in the center of a circle Arc: A portion of a circle Arc.

+ Circles and Arcs Objective: To find the measure of central angles and arcs. To find circumference and arc length.

Section 11-5 Areas of Circles and Sectors. Area of a Circle The area of a circle is times the square of the radius. Formula:

Arc Length and Sector Area. How do we get the fraction in these formulas? How many degrees are in a circle? Fraction = (central angle/360)

RADIANS Radians, like degrees, are a way of measuring angles.

Geometry Honors Section 5.3 Circumference and Area of Circles

7.2 – Sectors of Circles Essential Question: How do you find the radius of a sector given its’ area and arc length?

11.5 Sectors and Arc Lengths

Area Circumference Sectors

Geometry Honors Section 5.3 Circumference and Area of Circles.

Objective After studying this section, you will be able to begin solving problems involving circles 9.2 Introduction to Circles.

Chapter 4-2: Lengths of Arcs and Areas of Sectors.

Sector of a Circle Section  If a circle has a radius of 2 inches, then what is its circumference?  What is the length of the arc 172 o around.

AGENDA KAHOOT REVIEW LESSON 81 WORK TIME. LESSON 81: CENTRAL ANGLES AND ARCS Central Angle: an angle whose vertex is the center of the circle.

Lesson 11-6 Arc Lengths and Areas of Sectors (page 452) Essential Question How can you calculate the area of any figure?

10-7 Area of Circles and Sectors. REVIEW Circumference: The total distance (in length) around a circle. Arc measure: The measure of the central angle.

Area Circumference Sectors

A little more practice You’ve got this! High five!

Arcs, Sectors & Segments

11.6 Areas of Circles, Sectors, and Segments

Sector Area and Arc Length

Sector Area and Arc Length

Aim: How do we define radians and develop the formula

Bellwork 4/7/17.

11.6 Arc Lengths and Areas of Sectors

11.3 Areas of Circles and Sectors

Proportions in Circles

Arc length and area of a sector.

11-6: Arc Lengths and Areas of Sectors

16.2 Arc Length and Radian Measure

11.3 Sector Area and Arc Length (Part 1)

Concentric and Tangent Circles

Measuring Angles in Radians

Arc Length and Sector Area

End of 10.6 and All of 10.7.

12.3 Sector Area and Arc Length

9-2 and 11-3: Perimeter and Area of Circles and Sectors

4.1 Equations of circles Arcs, Inscribed Angles, Central Angles

Questions over hw?.

Bell Ringer 1. What is the proportion to determine arc length?

Questions over hw?.

Sector Area and Arc Length

Bell work week 20 (week 18/19 winter break)

Trigonometry - Intro Ms. Mougharbel.

Sector Area and Arc Length

Section Name: Arc Length & Area of Sector

Lesson 8-2 Formulas Circumference Arc Length Area Sector.

Essential Questions: Standards:

Areas of Plane Figures 11-6 Arc Lengths and Areas of Sectors

Warm up: Solve for x 1.) 2.) 4.) 3.) 124◦ 70◦ x 18◦ x 260◦ x 20◦ 110◦

Learning Target #20 Arc Length and Sector Areas

Here are some of the new justifications:

Presentation transcript:

Arc Lengths and Areas of Sectors Geometry Arc Lengths and Areas of Sectors

Arc Length The length of part of the circumference. The length of the arc depends on what two things? 1) The measure of the arc. 2) The size of the circle. An arc length measures distance while the measure of an arc is in degrees.

Sector of a circle A region bounded by 2 radii and an arc. .

 Portions of a Circle: Determine the Arc measure based on the portion given. 1/3 of circumference : 6π out of a total 36π on the circle: ¼ ● 360 ½ ● 360 1/3 ● 360 1/6 ● 360

Area of a Sector Formula measure of the central angle or arc m πr2 Area of a sector = 360 The area of the entire circle! The fraction of the circle! .

m 2πr 360 . Arc Length Formula measure of the central angle or arc The circumference of the entire circle! 2πr Arc Length = 360 The fraction of the circle! .

Find the length of AB and the area of sector AOB. 1. 2. 3. 4. 5. Length of AB Area of sector AOB B 90o B 90o 240o 300o 12 120o 108o O B O A A O A A 6 12 O 2.4 O 10√2 B B Fraction of circle: Fraction of circle: Fraction of circle: Fraction of circle: Fraction of circle: ¼ 2/3 5/6 1/3 3/10 Fraction ● circumference Fraction ● circumference Fraction ● circumference ¼ ● 12π 2/3 ● 24π 5/6 ● 24π 1/3 ● 4.8π 3/10 ● 20√2π 3π units 16π units 20π units 1.6π units 6√2π units Fraction ● area Fraction ● area Fraction ● area Fraction ● area Fraction ● area ¼ ● 36π 2/3 ● 144π 5/6 ● 144π 1/3 ● 5.76π 3/10 ● 200π 9π units2 96π units2 120π units2 1.92π units2 60π units2

6. The area of sector AOB is 48π and . Find the radius of ○O. m πr2 Area of a sector = 360 270 48π = πr2 360 4 16 3 4 r2 48 = 3 4 3 r2 64 = r = 8

7. The area of sector AOB is and . Find the radius of ○O. m πr2 Area of a sector = 360 9 40 π = πr2 4 360 9 9 1 9 = r2 1 4 9 1 81 = r2 4 9 r = 2

Find the area of the shaded region Find the area of the shaded region. Point O marks the center of the circle. 8. 9. 10. 11. 60˚ 8 12 60 O 6 4 30 O O 160 π units2 9π - 18 units2 24π - 36√3 units2 8π - 8√3 units2 3

HW Khan academy Due Tuesday march 6th at 8am Quiz Tuesday/Wednesday over arc length and sector area

Some common fractions and measures! Arc or Central Angle Measure Fraction of the Circle 36o 108o 1/6 5/6 120o 2/3 30o 11/12 1/8 5/8 3/10 1/10 60o 300o 1/3 240o 1/12 330o 45o 225o