iGCSE Mathematics (0580) - C5.3 Circles, arcs and sectors- Exam Style Questions Paper 3- New Syllabus

(a)
The diameter of the pond is $10\text{ m}$, so the radius is $5\text{ m}$. The total area of the full circular pond is:
$\text{Area} = \pi \times 5^2$
$\text{Area} \approx 78.5\text{ m}^2$
✅ Answer: 78.5

(b)
The diagram implies half of the circular pond intrudes into the rectangle, creating the grass area. First, find the total area of the $10\text{ m}$ by $16\text{ m}$ rectangle, then subtract half the area of the pond.
$\text{Area of rectangle} = 10 \times 16 = 160$
$\text{Grass Area} = 160 – (\frac{1}{2} \times 78.54)$
$\text{Grass Area} = 160 – 39.27 = 120.7\text{ m}^2$
✅ Answer: 120.7

(c)
The total area of the garden is the area of the grass plus the area of the pond inside the garden outline (the rectangle), which is exactly the area of the $10 \times 16$ rectangle.
$\text{Percentage} = (\frac{120.73}{160}) \times 100 \approx 75.5\%$
✅ Answer: 75.5