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

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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

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