Circumference, arc length, sector area
AQA GCSE Maths revision on Circumference, arc length, sector area. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.
Sample questions (3 of 16)
-
Question 1
A student claims that doubling the radius of a circle doubles its circumference. Why is this statement correct?
- A) The circumference is directly proportional to the radius.
- B) The circumference is proportional to the square of the radius.
- C) The circumference is inversely proportional to the radius.
- D) The circumference is independent of the radius.
Show answer
Answer: The circumference is directly proportional to the radius.
The formula for circumference is C = 2 * pi * r. Because 2 and pi are constants, the circumference scales linearly with the radius, meaning any change to the radius is mirrored exactly in the circumference.
-
Question 2
When calculating the area of a sector, what geometric property must be used alongside the radius?
- A) The chord length
- B) The central angle
- C) The tangent length
- D) The diameter
Show answer
Answer: The central angle
A sector is a proportional slice of a circle. The central angle tells you the ratio of the sector's area to the total area of the circle, which is defined as the angle divided by 360 degrees.
-
Question 3
If you are given the arc length and the radius of a circle, what is the first step to find the central angle?
Show answer
Answer: Rearrangement
The arc length formula is (angle/360) * 2 * pi * r. To find the angle, you must first rearrange the algebraic equation to make the angle the subject before substituting the known values.
Want to test yourself on the remaining cards for this topic?
13 more questions on Circumference, arc length, sector area — plus mistakes tracking and spaced repetition across the whole Maths spec.