Arc Length & Sector Area

Front

What is the formula for the area of a sector?

Back

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

Front

How do you calculate the arc length of a circle?

Back

The arc length \( L \) can be calculated using the formula: \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

What is the relationship between the radius and the arc length?

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases for a given central angle.

Front

If the radius of a circle is 10 cm and the central angle is 90°, what is the arc length?

Back

Using the formula \( L = \frac{\theta}{360} \times 2\pi r \): \( L = \frac{90}{360} \times 2\pi(10) = 15.7 \text{ cm} \) (approximately).

Front

What is the area of a sector with a radius of 5 m and a central angle of 60°?

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \): \( A = \frac{60}{360} \times \pi(5^2) = \frac{25\pi}{3} \text{ m}^2 \) (approximately 26.2 m²).

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 formula for the area of a circle?

Back

The area of a circle is given by the formula: \( A = \pi r^2 \), where \( r \) 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

If the central angle of a sector is 180°, what fraction of the circle does it represent?

Back

A central angle of 180° represents half of the circle, or \( \frac{1}{2} \) of the total area.

Front

What is the formula for the circumference of a circle?

Back

The circumference \( C \) of a circle is given by the formula: \( C = 2\pi r \), where \( r \) is the radius.