Area of a Segment

Front

What is the area of a segment in a circle?

Back

The area of a segment is the area of the sector minus the area of the triangle formed by the two radii and the chord.

Front

How do you calculate the area of a sector?

Back

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

Front

What is a segment in a circle?

Back

A segment is the area of a circle that is 'cut off' from the rest of the circle by a chord.

Front

What is the formula for the area of a triangle given two sides and the included angle?

Back

Area = 0.5 × a × b × sin(θ), where a and b are the lengths of the sides and θ is the included angle.

Front

If the radius of a circle is 5 cm and the angle of the sector is 60 degrees, what is the area of the sector?

Back

Area = (60/360) × π × (5)² = 13.09 cm².

Front

What is the relationship between the radius and the area of a segment?

Back

As the radius increases, the area of the segment also increases, assuming the angle remains constant.

Front

How do you find the length of an arc?

Back

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

Front

What is the area of a circle with a radius of 4 cm?

Back

Area = πr² = π × (4)² = 50.27 cm².

Front

What is the difference between a sector and a segment?

Back

A sector is a 'pie slice' of a circle, while a segment is the area between a chord and the arc it subtends.

Front

If the area of a sector is 20 cm² and the radius is 5 cm, what is the angle of the sector?

Back

θ = (Area × 360) / (πr²) = (20 × 360) / (π × 25) = 153.94 degrees.