Understanding Sector Area Calculations

Front

What is the formula for the area of a sector?

Back

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

Front

How do you calculate the area of a sector when given the radius and central angle?

Back

Use the formula: Area = (θ/360) × πr².

Front

If the radius of a circle is 10 inches and the central angle is 90°, what is the area of the sector?

Back

Area = (90/360) × π(10)² = 25π in².

Front

What is the area of a sector with a radius of 5 inches and a central angle of 60°?

Back

Area = (60/360) × π(5)² = (1/6) × 25π = (25/6)π in².

Front

What does the term 'central angle' refer to in a circle?

Back

The central angle is the angle whose vertex is at the center of the circle and whose sides intersect the circle.

Front

How do you convert degrees to radians for sector area calculations?

Back

Radians = Degrees × (π/180).

Front

What is the area of a sector with a radius of 8 inches and a central angle of 45°?

Back

Area = (45/360) × π(8)² = (1/8) × 64π = 8π in².

Front

If a sector has an area of 20π in² and a radius of 10 inches, what is the central angle?

Back

θ = (Area × 360)/(πr²) = (20π × 360)/(π(10)²) = 72°.

Front

What is the relationship between the area of a sector and the area of the entire circle?

Back

The area of the sector is a fraction of the area of the entire circle, determined by the ratio of the central angle to 360°.

Front

How do you find the area of a shaded region that includes a sector?

Back

Subtract the area of the triangle formed by the radii from the area of the sector.