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Catholic High 2025 P6 Maths Prelim — Paper 1 Booklet A Q14 Solution

Paper 1 Booklet A · Q14 · 2 marks · Area and Perimeter

Question

The figure is made up of one big semicircle and a small semicircle. The large semicircle with centre O has a radius of 6 cm. Find the perimeter of the figure. Leave your answer in terms of $\pi$.

1. $6\pi \text{ cm}$
2. $9\pi \text{ cm}$
3. $(6\pi + 6) \text{ cm}$
4. $(9\pi + 6) \text{ cm}$

Answer: 4

Worked solution

$\text{Big semicircle arc} = \pi \times 6 = 6\pi \text{ cm}$
$\text{Small semicircle radius} = 12 \div 2 \div 2 = 3 \text{ cm}$
$\text{Small semicircle arc} = \pi \times 3 = 3\pi \text{ cm}$
$\text{Exposed straight edge} = 6 \text{ cm}$
$\text{Perimeter} = 6\pi + 3\pi + 6 = (9\pi + 6) \text{ cm}$

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