Arc Length and Sector Area

Front

What is an arc?

Back

An arc is a smaller piece of the circumference of a circle.

Front

What is the length of an arc called?

Back

The length of an arc is called the arc length.

Front

What is a sector in a circle?

Back

A sector is the area enclosed by two radii and the arc between them.

Front

How do you calculate the area of a sector?

Back

Area of a sector = (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

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

Front

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

Back

The arc length increases with an increase in the radius for a given central angle.

Front

What is the difference between a sector and a segment?

Back

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

Front

If the radius of a circle is 10 cm and the central angle is 60 degrees, what is the arc length?

Back

Arc length = (60/360) × 2π(10) = 10.47 cm.

Front

What is the area of a sector with a radius of 5 cm and a central angle of 90 degrees?

Back

Area = (90/360) × π(5)² = 19.63 cm².

Front

What is the formula to find the area of a circle?

Back

Area of a circle = πr², where r is the radius.