iGCSE Mathematics (0580) : C5.3 Carry out calculations involving the circumference and area of a circle. iGCSE Style Questions Paper 1

Question

The diagram shows a sector of a circle with radius 4.8 cm and sector angle 45°.

Calculate the area of the sector.

▶️ Answer/Explanation

Solution

Ans: 9.05 cm² (or 9.04-9.06)

Area of full circle = π × 4.8² ≈ 72.382 cm².

Sector area = (45/360) × 72.382 ≈ 9.048 cm².

Or directly: (π × 4.8² × 45)/360 ≈ 9.05 cm².

Question

The diagram shows a sector of a circle with radius r cm and sector angle 72°.
The arc length is 9.35 cm.

Calculate the value of r.

▶️ Answer/Explanation

Solution

Ans: 7.44

Arc length = (θ/360) × 2πr

9.35 = (72/360) × 2 × 3.142 × r

9.35 = 0.2 × 6.284 × r

r = 9.35 ÷ 1.2568 ≈ 7.44

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