Arcs and Sectors

Front

What is an arc in a circle?

Back

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

Front

What is a sector in a circle?

Back

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

Front

How do you calculate the angle of a sector?

Back

The angle of a sector can be calculated using the formula: (Arc Length / Radius) x (180/π).

Front

What is the formula for the length of an arc?

Back

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

Front

What is the formula for the area of a sector?

Back

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

Front

If the angle of a sector is 144 degrees, what fraction of the circle does it represent?

Back

144 degrees represents 144/360 = 2/5 of the circle.

Front

What is the relationship between the angle of a sector and the area of the sector?

Back

The area of a sector is directly proportional to the angle of the sector.

Front

How do you find the central angle of a sector if you know the arc length and radius?

Back

Central Angle (in degrees) = (Arc Length / Radius) x (360/2π).

Front

What is the total angle in a circle?

Back

The total angle in a circle is 360 degrees.

Front

If the radius of a circle is 3 yards, what is the area of a sector with a 90-degree angle?

Back

Area = (90/360) x π(3)² = (1/4) x 9π = 2.25π yd².