Area of 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

What is a sector 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 find the radius if you know the diameter?

Back

Radius = Diameter / 2.

Front

What is the relationship between degrees and radians?

Back

180 degrees = π radians.

Front

If the radius of a circle is 10 inches, what is the area of the entire circle?

Back

Area = πr² = π(10)² = 100π ≈ 314.16 square inches.

Front

What is the area of a sector with a radius of 5 inches and a central angle of 90 degrees?

Back

Area = (90/360) × π(5)² = (1/4) × 25π ≈ 19.63 square inches.

Front

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

Back

Area = (45/360) × π(8)² = (1/8) × 64π ≈ 25.13 square inches.

Front

How do you convert degrees to radians?

Back

Multiply degrees by (π/180).

Front

What is the area of a sector with a radius of 12 inches and a central angle of 120 degrees?

Back

Area = (120/360) × π(12)² = (1/3) × 144π ≈ 150.80 square inches.

Front

What is the area of a sector with a radius of 3 inches and a central angle of 60 degrees?

Back

Area = (60/360) × π(3)² = (1/6) × 9π ≈ 4.71 square inches.