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

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

What does the variable $$\theta$$ represent in the equation $$s = \theta r$$ ?

In the equation $$s = \theta r$$ , $$\theta$$ represents the central angle measured in radians.

If the length of an arc is 15.8π ft, what is the radius if the central angle is 45 degrees?

Convert 45 degrees to radians: $$\frac{45 \times \text{π}}{180} = \frac{\text{π}}{4}$$ . Then, use the formula: $$r = \frac{s}{\theta} = \frac{15.8\text{π}}{\frac{\text{π}}{4}} = 63.2 \text{ ft}$$ .

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

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

How do you find the central angle if the area of the sector and radius are known?

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

What is the formula for the circumference of a circle?

The circumference of a circle is given by the formula: $$C = 2\text{π} r$$ , where $$r$$ is the radius.

If a sector has an area of 25π in² and a radius of 5 inches, what is the central angle in radians?

Using the area formula: $$A = \frac{1}{2} r^2 \theta$$ , we can solve for $$\theta$$ : $$\theta = \frac{2A}{r^2} = \frac{2(25\text{π})}{(5)^2} = 2\text{π} \text{ radians}$$ .

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

The area of a sector increases with the square of the radius, as seen in the formula: $$A = \frac{1}{2} r^2 \theta$$ .

Resource Library

Math

Trigonometry

Radians And Arc Length

Arcs And Sectors Flashcard Review

Arcs and Sectors Flashcard Review

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Mathematics

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11th Grade

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Practice Problem

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Hard

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FLASHCARD QUESTION

Front

What is the formula for the area of a sector?

Back

FLASHCARD QUESTION

Front

How do you find the length of an arc in a circle?

Back

FLASHCARD QUESTION

Front

What is the relationship between degrees and radians?

Back

FLASHCARD QUESTION

Front

If the central angle of a sector is 90 degrees, what is its radian measure?

Back

FLASHCARD QUESTION

Front

What is the area of a circle with a radius of 5 inches?

Back

FLASHCARD QUESTION

Front

How do you calculate the area of a shaded sector given the radius and central angle?

Back

FLASHCARD QUESTION

Front

What is the formula to find the radius if the arc length and central angle are known?

Back

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