Flashcardizz: Area of a Sector

Front

What is the formula for the area of a sector?

Back

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

Front

What does the term 'sector' refer to in a circle?

Back

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

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 the relationship between the radius and the area of a sector?

Back

The area of a sector increases with the square of the radius.

Front

If the radius of a circle is 7 cm, what is the area of a sector with a 90-degree angle?

Back

Area = (90/360) × π(7)² = 38.48 cm².

Front

What is the significance of the angle in calculating the area of a sector?

Back

The angle determines the proportion of the circle that the sector represents.

Front

What is the area of a sector with a radius of 5 cm and an angle of 60 degrees?

Back

Area = (60/360) × π(5)² = 13.09 cm².

Front

What is the unit of measurement for area?

Back

Common units include square centimeters (cm²), square meters (m²), and square inches (in²).

Front

How does the area of a sector compare to the area of the entire circle?

Back

The area of a sector is a fraction of the area of the entire circle, based on the angle.

Front

What is the area of a sector with a radius of 10 cm and an angle of 180 degrees?

Back

Area = (180/360) × π(10)² = 157.08 cm².