10.2 Area of Sectors

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

How do you find the angle of a sector given the arc length and radius?

Back

θ = (arc length / radius) × (180/π) in degrees.

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 doubled, how does the area of the sector change?

Back

The area of the sector increases by a factor of four.

Front

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

Back

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

Front

How do you express the area of a sector in terms of π?

Back

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

Front

What is the area of a sector with a radius of 3 units and an arc length of 4.71 units?

Back

Area = (arc length × radius) / 2 = (4.71 × 3) / 2 = 7.065 square units.

Front

What is the area of a sector with a radius of 4 units and an angle of 90 degrees?

Back

Area = (90/360) × π(4)² = (1/4) × 16π = 4π square units.

Front

How do you calculate the area of a shaded region in a circle?

Back

Subtract the area of the unshaded part from the total area of the circle.

Front

What is the area of a sector with a radius of 6 units and an angle of 120 degrees?

Back

Area = (120/360) × π(6)² = (1/3) × 36π = 12π square units.