Arc Length and Area of Sector

Front

What is the formula for arc length in a circle?

Back

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

Front

What is the formula for the area of a sector in a circle?

Back

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

Front

Define 'arc length'.

Back

Arc length is the distance along the curved line of a circle's circumference between two points.

Front

Define 'sector of a circle'.

Back

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

Front

What is the relationship between the angle and arc length in a circle?

Back

The arc length is directly proportional to the angle subtended at the center of the circle.

Front

How do you convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

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

Back

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

Front

If a circle has a radius of 5 m and a central angle of 90 degrees, what is the area of the sector?

Back

Area of Sector = (90/360) * π(5)² = 19.63 m².

Front

What is the total angle in a circle?

Back

The total angle in a circle is 360 degrees.

Front

What is the circumference of a circle with a radius of 7 inches?

Back

Circumference = 2πr = 2π(7) = 43.98 inches.