Arc Length and Sector Area Flashcard

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 formula for the area of a sector?

Back

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

Front

Define 'central angle'.

Back

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

Front

What is a 'sector' in a circle?

Back

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

Front

What is an 'arc' in a circle?

Back

An arc is a portion of the circumference of a circle.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

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

Back

Arc Length = (60/360) * 2π(10) = 10.47 cm.

Front

If the radius of a circle is 5 inches and the central angle is 90°, what is the area of the sector?

Back

Area of Sector = (90/360) * π(5)² = 19.63 sq. in.

Front

What is the difference between a sector and a segment?

Back

A sector is a part of a circle enclosed by two radii and an arc, while a segment is a region bounded by a chord and the arc connecting its endpoints.

Front

Calculate the area of a sector with a radius of 8 cm and a central angle of 45°.

Back

Area of Sector = (45/360) * π(8)² = 11.78 sq. cm.