Question 1: Calculate the central angle of a sector that subtends an arc length of 15 cm in a circle with radius 10 cm. Show your working.

Answer: 54

Question 2: A sector has a central angle of 60° in a circle of radius 12 cm. Find the area of the sector.

Answer: 37.7

Question 3: If a sector's area is 50 cm² and the radius of the circle is 10 cm, what is the measure of the central angle? Show your working.

Answer: 57.3

Question 4: A student mistakenly uses the entire circle's area when calculating the sector's area. Identify the error and explain how to correct it.

Answer: They used total circle area instead of sector area; fix by multiplying the sector's angle proportion by the circle's total area.

Question 5: Construct a sector with a radius of 9 cm and a central angle of 90°. Calculate the area of the sector and verify your result by drawing.

Answer: 113.1

Question 6: A sector with radius 15 cm has an area of 157.08 cm². What is the central angle? Show your working.

Answer: 60

Question 7: A student claims that doubling the radius doubles the area of the sector. Is this correct? Justify your answer.

Answer: No, because area depends on radius squared; doubling radius increases area by a factor of four.

Question 8: A sector with a central angle of 45° in a circle with radius 20 cm has an area of approximately 44.2 cm². Identify any error in this statement and correct it.

Answer: The calculated area is incorrect; correct area is 44.2 cm², but the error may be in the calculation of the angle or area formula used.

Question 9: A sector's central angle is 120° and radius is 8 cm. Calculate the sector's area and verify whether the area is correct based on your calculations.

Answer: 21.1

Question 10: In a circle, a sector has an arc length of 20 cm and radius 5 cm. What is the central angle? Show your working.

Answer: 91

Question 11: Identify and correct the mistake in this calculation: 'Sector area = (central angle/360) × π × r²; using central angle 90° and radius 10 cm, the area is 25π cm².'

Answer: The calculation is correct mathematically; however, the area in numerical form is approximately 78.5 cm², not 25π cm² (which is exact). The mistake is in interpreting the answer as an exact value rather than a decimal approximation.