What is the area of a sector with a radius of 7 cm and a central angle of 270 degrees?

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{270}{360} \times \text{π} \times 7^2 = \frac{3}{4} \times \text{π} \times 49 = \frac{147\text{π}}{4} \text{ cm}^2 \text{ (approximately 115.19 cm}^2)$$ .

What is the area of a sector with a radius of 4 cm and a central angle of 60 degrees?

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{60}{360} \times \text{π} \times 4^2 = \frac{1}{6} \times \text{π} \times 16 = \frac{8\text{π}}{3} \text{ cm}^2 \text{ (approximately 8.38 cm}^2)$$ .

What is the significance of the fraction $$\frac{x}{360}$$ in the area of a sector formula?

The fraction $$\frac{x}{360}$$ represents the proportion of the circle that the sector occupies, based on the central angle x.

If a sector has a central angle of 180 degrees, what fraction of the circle does it represent?

A sector with a central angle of 180 degrees represents half of the circle, or $$\frac{1}{2}$$ .

What is the area of a sector with a radius of 3 cm and a central angle of 120 degrees?

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{120}{360} \times \text{π} \times 3^2 = \frac{1}{3} \times \text{π} \times 9 = 3\text{π} \text{ cm}^2 \text{ (approximately 9.42 cm}^2)$$ .

What happens to the area of a sector if the radius is doubled?

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 area of a sector with a radius of 8 cm and a central angle of 45 degrees?

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{45}{360} \times \text{π} \times 8^2 = \frac{1}{8} \times \text{π} \times 64 = 8\text{π} \text{ cm}^2 \text{ (approximately 25.13 cm}^2)$$ .

What is the area of a sector with a radius of 5 cm and a central angle of 30 degrees?

Using the formula $$A = \frac{x}{360} \times \text{π} r^2$$ , we have: $$A = \frac{30}{360} \times \text{π} \times 5^2 = \frac{1}{12} \times \text{π} \times 25 = \frac{25\text{π}}{12} \text{ cm}^2 \text{ (approximately 6.54 cm}^2)$$ .

Area of a sector Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

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

Back

2.

FLASHCARD QUESTION

Front

What does the variable 'x' represent in the area of a sector formula?

Back

'x' represents the central angle of the sector in degrees.

3.

FLASHCARD QUESTION

Front

What is the area of a circle with radius r?

Back

4.

FLASHCARD QUESTION

Front

If the radius of a sector is 10 cm and the central angle is 90 degrees, what is the area of the sector?

Back

5.

FLASHCARD QUESTION

Front

How do you convert the area of a sector from square centimeters to square meters?

Back

To convert from square centimeters to square meters, divide the area in square centimeters by 10,000.

6.

FLASHCARD QUESTION

Front

What is the relationship between the angle of a sector and its area?

Back

The area of a sector is directly proportional to the central angle; as the angle increases, the area of the sector increases.

7.

FLASHCARD QUESTION

Front

If a sector has an area of 15 cm² and a radius of 5 cm, what is the central angle?

Back

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

14 questions

2025 S3/4 CCKS Nutrients

Flashcard

•

8th Grade - University

16 questions

IM gr7 Unit 4 Check point A

Flashcard

•

7th Grade - University

15 questions

English to Arabic Clothing Vocabulary

Flashcard

•

9th Grade - University

15 questions

Roman Emperors: Strengths and Weaknesses

Flashcard

•

7th Grade - University

10 questions

Purpose Clauses

Flashcard

•

10th - 11th Grade

10 questions

Vocabulary Flashcards

Flashcard

•

KG - University

9 questions

Parts of a Computer

Flashcard

•

9th - 12th Grade

13 questions

[AP CSP] Binary Conversion

Flashcard

•

9th - 12th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

20 questions

Figurative Language Review

Quiz

•

6th Grade

Discover more resources for Mathematics

15 questions

Product of Powers Property A1 U7

Quiz

•

8th Grade

20 questions

Laws of Exponents

Quiz

•

8th Grade

16 questions

8th U5L5 Graphs of Functions

Quiz

•

8th Grade

20 questions

Graphing Inequalities on a Number Line

Quiz

•

6th - 9th Grade

12 questions

Exponential Growth and Decay

Quiz

•

9th Grade

20 questions

Exponent Rules Review

Quiz

•

8th - 9th Grade

20 questions

One Step equations addition and subtraction

Quiz

•

5th - 8th Grade

20 questions

Translations

Quiz

•

8th Grade