Area Of A Sector -Multiple Choice Questions Quiz

Question 1: What is the formula to calculate the area of a sector with radius 'r' and central angle 'θ' (in radians)?

(a) Area = r × θ
(b) Area = 2 × π × r × θ
(c) Area = 0.5 × r^2 × θ
(d) Area = (θ/360) x π × r^2

Question 2: A sector has a central angle of 45 degrees (π/4 radians) and a radius of 8 meters. What is its area?

(a) 8 square meters
(b) 16 square meters
(c) 32 square meters
(d) 64 square meters

Question 3: In a circle of radius 10 cm (0.1 m), a central angle of 60 degrees (π/3 radians) subtends an arc. What is the area of the sector formed by this angle?

(a) π/300 square meters
(b) π/600 square meters
(c) 30π square meters
(d) 40π square meters

Question 4: If the area of a sector is 25 square units and the radius is 5 units, what is the measure of the central angle (in radians)?

(a) π radians
(b) 2 radians
(c) 6π radians
(d) 14 radians

Question 5: The area of a sector of a circle is 100π square inches, and the central angle is 90 degrees (π/2 radians). What is the radius of the circle?

(a) 5 inches
(b) 10 inches
(c) 20 inches
(d) 50 inches

Question 6: In a circle, the area of a sector is one-fourth of the entire circle's area. What is the measure of the central angle (in radians)?

(a) π/2 radians
(b) π radians
(c) 2π radians
(d) 4π radians

Question 7: A sector of a circle has a central angle of 120 degrees (2π/3 radians) and an area of 108π square units. What is the radius of the circle?

(a) 3 units
(b) 6 units
(c) 9 units
(d) 18 units

Question 8: If the area of a sector is 64π square centimeters and the central angle is 900 degrees (π/2 radians), what is the radius of the circle?

(a) 4 centimeters
(b) 8 centimeters
(c) 16 centimeters
(d) 32 centimeters

Question 9: The area of a sector is 100π square units, and the central angle is 360 degrees (2π radians). What is the radius of the circle?

(a) 5 units
(b) 10 units
(c) 20 units
(d) 50 units

Question 10: In a circle with radius 6 meters, a sector's area is 36π square meters. What is the measure of the central angle (in radians)?

(a) π/6 radians
(b) π/3 radians
(c) 2π radians
(d) π radians

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Total score: /10

Answer key:

Question 1: c

Question 2: b

Question 3: b

Question 4: b

Question 5: c

Question 6: a

Question 7: d

Question 8: c

Question 9: b

Question 10: c