Arc Length and Sector Area

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: \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

How do you calculate the arc length of a sector?

Back

The arc length \( L \) of a sector is 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 area of a sector?

Back

The area of a sector increases with the square of the radius. If the radius doubles, the area of the sector increases by a factor of four.

Front

If a circle has a radius of 10 cm and a central angle of 90°, what is the area of the sector?

Back

Using the formula, the area is: \( A = \frac{90}{360} \times \pi (10)^2 = 25\pi \, \text{cm}^2 \).

Front

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

Back

The area is: \( A = \frac{60}{360} \times \pi (5)^2 = \frac{25\pi}{6} \, \text{cm}^2 \).

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 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.

Front

How do you express the area of a sector in terms of \( \pi \)?

Back

The area of a sector can be expressed as: \( A = \frac{\theta}{360} \times r^2 \, \pi \), where \( \theta \) is the angle in degrees.

Front

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

Back

If the radius is halved, the area of the sector decreases by a factor of four, since area is proportional to the square of the radius.

Front

What is the area of a sector with a radius of 12 cm and a central angle of 150°?

Back

The area is: \( A = \frac{150}{360} \times \pi (12)^2 = 30\pi \, \text{cm}^2 \).