iGCSE Mathematics (0580) - C5.3 Circles, arcs and sectors- Exam Style Questions Paper 1- New Syllabus
▶️ Answer/Explanation
The perimeter of a semicircle consists of two parts: the curved arc and the straight diameter.
Curved arc (half the full circumference): \(\dfrac{1}{2} \times 2\pi r = \pi r = \pi \times 8 = 8\pi\)
Straight diameter: \(2r = 2 \times 8 = 16\)
\[\text{Perimeter} = 8\pi + 16 = 8(\pi + 2) \text{ cm}\]
✅ Answer: \(8\pi + 16\) cm (or equivalently \(8(\pi + 2)\) cm)
Curved arc (half the full circumference): \(\dfrac{1}{2} \times 2\pi r = \pi r = \pi \times 8 = 8\pi\)
Straight diameter: \(2r = 2 \times 8 = 16\)
\[\text{Perimeter} = 8\pi + 16 = 8(\pi + 2) \text{ cm}\]
✅ Answer: \(8\pi + 16\) cm (or equivalently \(8(\pi + 2)\) cm)
▶️ Answer/Explanation
First, find the radius by dividing the diameter by \(2\): \(r = \frac{16}{2} = 8 \text{ cm}\).
Use the formula for the area of a circle: \(A = \pi r^2\).
Substitute the radius into the formula: \(A = \pi \times 8^2 = 64\pi\).
✅ Answer: \(64\pi\)
▶️ Answer/Explanation
The area of a sector is determined by taking the ratio of its angle to a full $360^{\circ}$ turn, multiplied by the formula for a full circle’s area ($\pi r^2$): $$\text{Area} = \frac{\theta}{360^{\circ}} \times \pi r^2$$ $$\text{Area} = \frac{60}{360} \times \pi \times 3^2$$ $$\text{Area} = \frac{1}{6} \times \pi \times 9 = \frac{9}{6}\pi = \frac{3}{2}\pi$$
Answer: $\frac{3}{2}\pi$ or $1\frac{1}{2}\pi$ or 1.5$\pi$