Area of Sectors

Front

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

Back

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

Front

How do you find the radius of a circle if you know the diameter?

Back

The radius is half of the diameter. If \( d \) is the diameter, then \( r = \frac{d}{2} \).

Front

What is a central angle in a circle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circumference.

Front

If the radius of a circle is 10 cm, what is the area of the entire circle?

Back

The area of the circle is given by \( A = \pi r^2 = \pi (10)^2 = 100\pi \approx 314.16 \text{ cm}^2 \).

Front

What is the relationship between the area of a sector and the central angle?

Back

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

Front

How do you convert a central angle from 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 m and a central angle of 60°?

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \): \( A = \frac{60}{360} \times \pi (5)^2 = \frac{1}{6} \times 25\pi \approx 13.09 \text{ m}^2 \).

Front

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

Back

The area of a sector in radians is given by: \( A = \frac{1}{2} r^2 \theta \), where \( \theta \) is in radians.

Front

If a sector has an area of 50 cm² and a radius of 10 cm, what is the central angle in degrees?

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \), we can rearrange to find \( \theta = \frac{A \times 360}{\pi r^2} = \frac{50 \times 360}{\pi (10)^2} \approx 57.30° \).

Front

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

Back

Using the formula: \( A = \frac{90}{360} \times \pi (8)^2 = \frac{1}{4} \times 64\pi \approx 50.27 \text{ cm}^2 \).