Area and Sectors of a Circle

Front

What is the formula for the area of a circle?

Back

A = πr², where A is the area and r is the radius.

Front

How do you find the area of a sector of a circle?

Back

Area of sector = (θ/360) × πr², where θ is the central angle in degrees.

Front

What is the relationship between the radius and the area of a circle?

Back

The area increases with the square of the radius; doubling the radius increases the area by a factor of four.

Front

If the radius of a circle is 7 inches, what is its area?

Back

A = π(7)² = 49π square inches.

Front

What is a segment of a circle?

Back

A segment is the area of a circle 'cut off' by a chord.

Front

How do you calculate the area of a segment?

Back

Area of segment = Area of sector - Area of triangle formed by the radius and chord.

Front

What is the formula for the circumference of a circle?

Back

C = 2πr, where C is the circumference and r is the radius.

Front

What is the central angle of a full circle?

Back

The central angle of a full circle is 360 degrees.

Front

If a circle has an area of 324 square inches, what is the radius?

Back

r = √(A/π) = √(324/π) = 18 inches.

Front

What is the area of a sector with a radius of 6 inches and a central angle of 100°?

Back

Area = (100/360) × π(6)² = 10π square inches.