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 $$\theta = \frac{2A}{r^2}$$ .

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?

Back

2.

FLASHCARD QUESTION

Front

How do you convert degrees to radians?

Back

3.

FLASHCARD QUESTION

Front

What is the formula for the length of an arc?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

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.

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