How do you find the length of an arc given the radius and angle in degrees?

Convert the angle from degrees to radians and then apply the arc length formula: $$L = r \theta$$ .

What is the area of a sector with a radius of 24 feet and an angle of 165 degrees?

Convert 165 degrees to radians: $$165 \times \frac{\pi}{180} = \frac{11\pi}{12}$$ . Then, use the area formula: $$A = \frac{1}{2} \times 24^2 \times \frac{11\pi}{12} = 132\pi$$ .

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

The area of a circle is given by the formula: $$A = \pi r^2$$ .

What is the relationship between the radius and the length of an arc?

The length of an arc is directly proportional to the radius; as the radius increases, the arc length increases.

If the radius is doubled, how does the area of the sector change?

If the radius is doubled, the area of the sector increases by a factor of four, since area is proportional to the square of the radius.

What is the formula for converting radians to degrees?

To convert radians to degrees, use the formula: $$degrees = radians \times \frac{180}{\pi}$$ .

What is the area of a sector with radius 10 and angle 90 degrees?

Convert 90 degrees to radians: $$90 \times \frac{\pi}{180} = \frac{\pi}{2}$$ . Then, use the area formula: $$A = \frac{1}{2} \times 10^2 \times \frac{\pi}{2} = 25\pi$$ .

How do you find the angle of a sector if you know the area and radius?

Rearranging the area formula $$A = \frac{1}{2} r^2 \theta$$ gives $$\theta = \frac{2A}{r^2}$$ .

Resource Library

Math

Trigonometry

Radians And Arc Length

Arc Length And Sector Area

Arc length and sector area

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

•

Hard

Wayground Content

FREE Resource

Student preview

15 questions

Show all answers

FLASHCARD QUESTION

Front

What is the formula for the area of a sector?

Back

FLASHCARD QUESTION

Front

How do you convert degrees to radians?

Back

FLASHCARD QUESTION

Front

What is the formula for the length of an arc?

Back

FLASHCARD QUESTION

Front

If the radius is 6 and the angle is 150 degrees, what is the length of the arc?

Back

FLASHCARD QUESTION

Front

What is the area of a sector with radius 16 and angle 315 degrees?

Back

FLASHCARD QUESTION

Front

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

Back

FLASHCARD QUESTION

Front

What is the significance of the angle in the arc length formula?

Back

The angle determines the proportion of the circle that the arc represents; larger angles yield longer arcs.

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

10 questions

Secondary storage

Flashcard

•

9th - 11th Grade

8 questions

Unit 3.7 Firm's costs, Revenue & Objective

Flashcard

•

11th Grade

10 questions

Industrial Revolution and Marxism

Flashcard

•

10th Grade

11 questions

3D Design Vocabulary Flashcard

Flashcard

•

10th Grade

12 questions

Organic 2 Exam 4 Review

Flashcard

•

12 questions

WORD FORMATION - NOUN/VERB/ADJECTIVE

Flashcard

•

10th Grade

13 questions

Regular and Irregular Verbs

Flashcard

•

10th Grade

8 questions

CHILDREN 2 (1ST CLASS)

Flashcard

•

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

10 questions

Probability Practice

Quiz

•

4th Grade

15 questions

Probability on Number LIne

Quiz

•

4th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

6 questions

Appropriate Chromebook Usage

Lesson

•

7th Grade

10 questions

Greek Bases tele and phon

Quiz

•

6th - 8th Grade

Discover more resources for Mathematics

23 questions

TSI Math Vocabulary

Quiz

•

10th - 12th Grade

10 questions

Plotting Points on a Coordinate Plane: Quadrant 1 Essentials

Interactive video

•

6th - 10th Grade

10 questions

Exploring Abiotic and Biotic Factors in Ecosystems

Interactive video

•

6th - 10th Grade

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade

16 questions

Converting Improper Fractions to Mixed Numbers

Quiz

•

4th - 10th Grade

10 questions

Solving One Step Equations: Key Concepts and Techniques

Interactive video

•

6th - 10th Grade

10 questions

Special Right Triangles

Quiz

•

10th Grade

16 questions

Circle Vocabulary

Quiz

•

9th - 10th Grade