Arc Length and Sector Area

Front

What is the formula for the area of a sector?

Back

The area of a sector 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 the relationship between an arc and the circumference of a circle?

Back

An arc is a portion of the circumference of a circle.

Front

How do you find the length of an arc given the radius and the central angle?

Back

The length of an arc can be calculated using the formula: Arc Length = (θ/360) * 2 * π * r, where θ is the angle in degrees and r is the radius.

Front

What is the definition of a sector in a circle?

Back

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

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle can be calculated using the formula: C = 2 * π * r, where r is the radius.

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 relationship between the angle of a sector and its area?

Back

The area of a sector is directly proportional to the angle of the sector; as the angle increases, the area of the sector increases.

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply the radian measure by (180/π).

Front

What is the length of a minor arc?

Back

The length of a minor arc is the distance along the curve of the arc, which can be calculated using the arc length formula.

Front

What is the significance of the central angle in relation to the arc length?

Back

The central angle determines the proportion of the circle that the arc represents, affecting both the arc length and the area of the sector.