How do you convert degrees to radians?

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

If a circle has a radius of 8 cm, what is the circumference?

The circumference $$C$$ is calculated using the formula: $$C = 2\text{π}r = 2\text{π} \times 8 = 16\text{π} \text{ cm}$$ .

What is the area of a sector with a radius of 4 m and a central angle of 120°?

The area is: $$A = \frac{120}{360} \times \text{π} \times 4^2 = \frac{1}{3} \times 16\text{π} = \frac{16\text{π}}{3} \text{ m}^2$$ .

What is the formula for the length of an arc?

The length of an arc is given by the formula: $$L = \frac{\theta}{360} \times 2\text{π}r$$ .

If the central angle of a sector is 180° and the radius is 3 m, what is the arc length?

The arc length is: $$L = \frac{180}{360} \times 2\text{π} \times 3 = \text{π} \times 3 = 3\text{π} \text{ m}$$ .

What is the area of a sector with a radius of 10 inches and a central angle of 45°?

The area is: $$A = \frac{45}{360} \times \text{π} \times 10^2 = \frac{1}{8} \times 100\text{π} = 12.5\text{π} \text{ in}^2$$ .

How do you find the unmarked area of a sector?

To find the unmarked area, subtract the area of the marked sector from the total area of the circle.

If a circle has a radius of 12 ft, what is the area of the entire circle?

The area is: $$A = \text{π} \times 12^2 = 144\text{π} \text{ ft}^2$$ .

Arc Length and Sector Area Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the formula for the area of a sector of a circle?

Back

2.

FLASHCARD QUESTION

Front

How do you calculate the arc length of a sector?

Back

3.

FLASHCARD QUESTION

Front

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

Back

The area of a sector increases with the square of the radius. If the radius doubles, the area of the sector increases by a factor of four.

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

What is the area of a sector with a radius of 5 inches and a central angle of 60°?

Back

6.

FLASHCARD QUESTION

Front

Define the term 'central angle' in the context of a circle.

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides (rays) extend to the circumference.

7.

FLASHCARD QUESTION

Front

What is the formula for the area of a circle?

Back

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