Sector Area and Arc Length

Front

What is the area of a sector of a circle?

Back

The area of a sector is the region bounded by two radii and the arc between them. It can be calculated using the formula: Area = (θ/360) * π * r², where θ is the angle in degrees and r is the radius.

Front

What is arc length?

Back

Arc length is the distance along the curved line of an arc. It can be calculated using the formula: Arc Length = (θ/360) * 2πr, where θ is the angle in degrees and r is the radius.

Front

What is a sector of a circle?

Back

A sector of a circle is a region bounded by two radii and the arc connecting them.

Front

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

Back

The arc length is directly proportional to the radius of the circle. As the radius increases, the arc length increases for a given angle.

Front

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

Back

When the angle is in radians, the area of a sector can be calculated using the formula: Area = (1/2) * r² * θ, where r is the radius and θ is the angle in radians.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is calculated using the formula: C = 2πr, where r is the radius.

Front

What is the difference between a sector and a segment of a circle?

Back

A sector is the area bounded by two radii and an arc, while a segment is the area bounded by a chord and the arc connecting the endpoints of the chord.

Front

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

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

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

Back

The area of a circle is calculated using the formula: Area = πr², where r is the radius.

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. A larger angle results in a larger area.