Sector Area and Arc Length

Front

What is the formula for the area of a sector?

Back

Area = (θ/360) × πr², where θ is the angle in degrees and r is the radius.

Front

How do you calculate the length of an arc?

Back

Arc Length = (θ/360) × 2πr, where θ is the angle in degrees and r is the radius.

Front

What is a sector in a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

Define the term 'central angle'.

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii.

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.

Front

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

Back

The area of the sector quadruples because area is proportional to the square of the radius.

Front

What is the formula for the area of a circle?

Back

Area = πr², where r is the radius.

Front

How do you find the area of a shaded region in a circle?

Back

Subtract the area of the unshaded part from the total area of the circle.

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

How do you convert arc length to degrees?

Back

Use the formula: θ = (Arc Length / Circumference) × 360.