Arc Length and Sector Area

Front

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

Back

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

Front

How do you calculate the arc length of a sector?

Back

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

Front

What is a sector in a circle?

Back

A sector is a portion of a circle enclosed by two radii and the arc between them.

Front

Define the term 'arc' in the context of a circle.

Back

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

Front

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

Back

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

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 circumference of a circle with a radius of 7 cm?

Back

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

Front

How do you find the area of a shaded sector if the total area of the circle is known?

Back

Area of shaded sector = Total area of circle - Area of unshaded part.

Front

What is the formula for the area of a circle?

Back

Area = πr², where r is the radius.

Front

If a sector has an area of 20 cm² and a radius of 4 cm, what is the angle of the sector?

Back

θ = (Area × 360) / (πr²) = (20 × 360) / (π(4)²) = 90 degrees.