How do you find the central angle of a sector given its area and radius?

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

What is the area of a sector with a radius of 10 and a central angle of 60 degrees?

First convert 60 degrees to radians: $$60 \times \frac{\pi}{180} = \frac{\pi}{3}$$ . Then, use the area formula: $$A = \frac{1}{2} \times 10^2 \times \frac{\pi}{3} = \frac{50\pi}{3}$$ .

What is the formula for the circumference of a circle?

The circumference $$C$$ of a circle is given by the formula: $$C = 2\pi r$$ .

If a sector has an area of 15π and a radius of 5, what is the central angle in degrees?

Using the area formula, $$\theta = \frac{2A}{r^2} = \frac{2 \times 15\pi}{5^2} = \frac{60\pi}{25} = \frac{12\pi}{5}$$ . Convert to degrees: $$\frac{12\pi}{5} \times \frac{180}{\pi} = 432\degree$$ .

What is the definition of a radius?

A radius is a line segment from the center of a circle to any point on its circumference.

What is the area of a sector with a radius of 8 and a central angle of 90 degrees?

Convert 90 degrees to radians: $$90 \times \frac{\pi}{180} = \frac{\pi}{2}$$ . Then, use the area formula: $$A = \frac{1}{2} \times 8^2 \times \frac{\pi}{2} = 16\pi$$ .

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

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

If the arc length of a circle is 10 and the radius is 5, what is the central angle in radians?

Using the arc length formula, $$\theta = \frac{L}{r} = \frac{10}{5} = 2\text{ radians}$$ .

Circles: Arc Length and Sector Area Flashcards

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15 questions

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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 relationship between the radius and diameter of a circle?

Back

4.

FLASHCARD QUESTION

Front

What is the formula for arc length?

Back

5.

FLASHCARD QUESTION

Front

If the radius of a circle is 5, what is the diameter?

Back

6.

FLASHCARD QUESTION

Front

What is the area of a circle with a radius of 7?

Back

7.

FLASHCARD QUESTION

Front

What is a sector in a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

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