Arc Length and Area Sector

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 length of an arc?

Back

Arc Length = (θ/360) × 2πr, where θ is the central 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 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 central angle of a full circle in degrees?

Back

360 degrees.

Front

What is the formula for the circumference of a circle?

Back

Circumference = 2πr, where r is the radius.

Front

If the central angle of a sector is 90 degrees, what fraction of the circle does it represent?

Back

1/4 of the circle.

Front

How do you convert radians to degrees?

Back

Degrees = Radians × (180/π).

Front

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

Back

Area = (60/360) × π(5)² = (1/6) × 25π ≈ 13.09 cm².

Front

What is the length of an arc with a radius of 10 m and a central angle of 45 degrees?

Back

Arc Length = (45/360) × 2π(10) = (1/8) × 20π ≈ 7.85 m.