Arc Length and Sector Area

Front

What is the area of a sector of a circle?

Back

The area of a sector is the portion of the circle enclosed by two radii and the arc between them. It can be calculated using the formula: Area = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

What is the formula for arc length?

Back

The arc length (L) of a circle can be calculated using the formula: L = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Front

Define 'sector' in the context of circles.

Back

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

Front

What is a 'segment' in a circle?

Back

A segment is a region of a circle that is bounded by a chord and the arc that connects the endpoints of the chord.

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

How do you find the area of a sector given the radius and central angle?

Back

Use the formula: Area = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

What is the central angle of a full circle?

Back

The central angle of a full circle is 360 degrees.

Front

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

Back

Area = (90/360) * π(10)² = (1/4) * 100π = 25π cm².

Front

What is the difference between a sector and a segment?

Back

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

Front

How do you express the area of a sector in terms of π?

Back

The area of a sector can be expressed as Area = (θ/360) * πr², where θ is the central angle in degrees.