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Calculations involving circumference, area, arc length, and sector area of a circle.
Diagram Description
Circle with radius 7 cm and central angle 60°
A circle has radius 7 cm. A sector of the circle has a central angle of 60°. Calculate the circumference, area, arc length of the sector, and the area of the sector. Express all answers in terms of π where appropriate.
| Quantity | Formula | Calculation | Answer |
|---|---|---|---|
| Circumference | 2πr | 2 × π × 7 | 14π cm |
| Area | πr² | π × 7² | 49π cm² |
| Arc length | (θ/360) × 2πr | (60/360) × 2 × π × 7 | (1/6) × 14π = 14π/6 = 7π/3 cm |
| Sector area | (θ/360) × πr² | (60/360) × π × 7² | (1/6) × 49π = 49π/6 cm² |
- a[1]
Calculate the circumference of the circle in terms of π.
Aim for approximately 1 distinct marking point.
- b[1]
Calculate the area of the circle in terms of π.
Aim for approximately 1 distinct marking point.
- c[2]
Calculate the length of the arc corresponding to the 60° sector, in terms of π.
Aim for approximately 2 distinct marking points.
- d[2]
Calculate the area of the sector with central angle 60°, in terms of π.
Aim for approximately 2 distinct marking points.
0 of 4 parts answered
Answer every part before opening the mark scheme.
Maths method check
- Topic focus: Circles, arcs and sectors.
- Question style: structured_mathematics.
- Reasoning demand: reasoning.
- Check the operation, notation, units, and final answer form against the question before moving on.
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