Sector Area

Front

What is the formula for the area of a sector?

Back

The area of a sector is given by the formula: \( A = \frac{\theta}{360} \times \pi r^2 \) for degrees or \( A = \frac{1}{2} r^2 \theta \) for radians, where \( \theta \) is the angle in degrees or radians and \( r \) is the radius.

Front

Define a sector in a circle.

Back

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

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 angle of the sector. As the angle increases, the area of the sector increases.

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: \( radians = degrees \times \frac{\pi}{180} \).

Front

If the radius of a circle is doubled, how does the area of the sector change?

Back

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.

Front

Calculate the area of a sector with a radius of 5 cm and an angle of 60 degrees.

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \): \( A = \frac{60}{360} \times \pi (5)^2 = \frac{1}{6} \times 25\pi \approx 13.1 \text{ cm}^2 \).

Front

What is the area of a sector with a radius of 10 m and an angle of 90 degrees?

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \): \( A = \frac{90}{360} \times \pi (10)^2 = \frac{1}{4} \times 100\pi \approx 78.5 \text{ m}^2 \).

Front

What is the area of a sector with a radius of 7 cm and an angle of 120 degrees?

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \): \( A = \frac{120}{360} \times \pi (7)^2 = \frac{1}{3} \times 49\pi \approx 51.8 \text{ cm}^2 \).

Front

What is the formula to find the angle in radians given the area of a sector?

Back

The angle in radians can be found using the formula: \( \theta = \frac{2A}{r^2} \) where \( A \) is the area of the sector and \( r \) is the radius.

Front

If a sector has an area of 25 cm² and a radius of 5 cm, what is the angle in radians?

Back

Using the formula \( \theta = \frac{2A}{r^2} \): \( \theta = \frac{2 \times 25}{5^2} = \frac{50}{25} = 2 \text{ radians} \).