Exploring Areas of Circles, Sectors, and Segments

What is the area of a sector with a radius of 9 units and an arc measure of 120 degrees?

• 9π units squared

• 81π units squared

• 27π units squared

• 54π units squared

What is the formula to calculate the area of a sector?

• Area of the circle × (measure of the arc / 360)

• Area of the circle × (measure of the arc / 180)

• Area of the circle × (measure of the arc / 90)

• Area of the circle × (measure of the arc / 720)

If the inscribed angle is 15 degrees, what is the measure of the intercepted arc?

• 30 degrees

• 60 degrees

• 15 degrees

• 45 degrees

For a circle with radius 12, what is the area of a sector with a 30-degree arc?

• 36π units squared

• 6π units squared

• 24π units squared

• 12π units squared

How do you calculate the area of a segment formed by a 90-degree arc in a circle with radius 16?

• 128π - 64 units squared

• 64π - 128 units squared

• 32π - 64 units squared

• 64π - 32 units squared

How do you find the area of a segment?

• Area of the triangle / area of the sector

• Area of the sector - area of the triangle

• Area of the sector + area of the triangle

• Area of the triangle - area of the sector

What is the area of a segment where the central angle is 60 degrees and the triangle is equilateral with sides of length 6?

• 9π - 18 units squared

• 18π - 9 units squared

• 9π - 6 units squared

• 6π - 9 units squared

What is the area of the shaded region if the side of the square is 12 and it includes one entire circle with radius 6?

• 180 - 72π units squared

• 144 - 72π units squared

• 180 - 36π units squared

• 144 - 36π units squared

What is the area of a circle with radius 6?

• 36π units squared

• 12π units squared

• 72π units squared

• 18π units squared

What is the area of the shaded region in a square with side 20, with an inscribed circle?

• 200 - 50π units squared

• 200 - 100π units squared

• 400 - 50π units squared

• 400 - 100π units squared