Circle Segments

Front

What is a circle segment?

Back

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

Front

How do you calculate the area of a circle segment?

Back

The area of a circle segment can be calculated using the formula: Area = (r^2/2) * (θ - sin(θ)), where r is the radius and θ is the central angle in radians.

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between the radius and the chord length in a circle segment?

Back

The length of the chord can be calculated using the formula: c = 2r * sin(θ/2), where r is the radius and θ is the central angle in radians.

Tags

CCSS.HSG.C.A.2

Front

What is the formula for the central angle of a circle segment given the chord length and radius?

Back

The central angle θ can be found using the formula: θ = 2 * arcsin(c/(2r)), where c is the chord length and r is the radius.

Tags

CCSS.HSG.C.A.2

Front

What is the difference between a circle segment and a sector?

Back

A circle segment is the area between a chord and the arc, while a sector is the area between two radii and the arc.

Front

How do you find the height of a circle segment?

Back

The height (h) of a circle segment can be calculated using the formula: h = r - (r * cos(θ/2)), where r is the radius and θ is the central angle in radians.

Tags

CCSS.HSG.SRT.C.8

Front

What is the formula for the area of a sector?

Back

The area of a sector can be calculated using the formula: Area = (1/2) * r^2 * θ, where r is the radius and θ is the central angle in radians.

Tags

CCSS.HSG.C.B.5

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: radians = degrees * (π/180).

Tags

CCSS.HSF.TF.A.1

Front

What is the significance of the central angle in circle segments?

Back

The central angle determines the size of the segment and is crucial for calculating the area and height of the segment.

Tags

CCSS.HSG.CO.C.9

Front

How can you find the length of the arc of a circle segment?

Back

The length of the arc can be calculated using the formula: Arc length = r * θ, where r is the radius and θ is the central angle in radians.

Tags

CCSS.HSG.C.B.5