Circles - Area of Sector

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

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 convert radians to degrees?

Back

Degrees = Radians × (180/π).

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 cm and an angle of 60 degrees?

Back

Area = (60/360) × π(5)² = (1/6) × 25π = 25π/6 cm².

Front

How do you find 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 total area of a circle with a radius of 10 cm?

Back

Area = πr² = π(10)² = 100π cm².

Front

What is the area of a sector with a central angle of 90 degrees and a radius of 4 m?

Back

Area = (90/360) × π(4)² = (1/4) × 16π = 4π m².

Front

What is the area of a sector with a central angle of 180 degrees and a radius of 3 m?

Back

Area = (180/360) × π(3)² = (1/2) × 9π = 4.5π m².