Geometry DOL Area of Sector

Front

What is the formula for the area of a sector in a circle?

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

How do you convert degrees to radians?

Back

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

Front

What is the area of a sector with a radius of 5 units and an angle of 120 degrees?

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \): \( A = \frac{120}{360} \times \pi (5^2) = \frac{1}{3} \times \pi \times 25 = \frac{25\pi}{3} \approx 26.18 \) units².

Front

What is the relationship between the angle in degrees and the area of the sector?

Back

The area of the sector is directly proportional to the angle. As the angle increases, the area of the sector increases.

Front

If a sector has an angle of 90 degrees, what fraction of the circle does it represent?

Back

A 90-degree angle represents \( \frac{90}{360} = \frac{1}{4} \) of the circle.

Front

What is the area of a sector with a radius of 12 units and an angle of 66 degrees?

Back

Using the formula: \( A = \frac{66}{360} \times \pi (12^2) \approx 82.94 \) units².

Front

How do you find the area of a sector when the angle is given in radians?

Back

Use the formula: \( A = \frac{1}{2} r^2 \theta \), where \( \theta \) is in radians.

Front

What is the area of a sector with a radius of 3 units and an angle of 134 degrees?

Back

Using the formula: \( A = \frac{134}{360} \times \pi (3^2) \approx 10.52 \) units².

Front

What is the significance of the radius in calculating the area of a sector?

Back

The radius is squared in the area formula, meaning that even small changes in the radius can significantly affect the area.

Front

What is the area of a sector with a radius of 30 feet and an angle of 120 degrees?

Back

Using the formula: \( A = \frac{120}{360} \times \pi (30^2) \approx 942.5 \) ft².