1. **Problem Statement:** We have a large semi-circle with radius 7 cm and a smaller semi-circle with diameter 7 cm cut out and reattached. We need to find: (i) The arc length of the sector of the circle with radius 7 cm. (ii) The arc length of the sector of the circle with diameter 7 cm. (iii) The perimeter of the shaded region formed after reattachment. 2. **Formulas and Rules:** - Arc length of a semi-circle (half circle) is given by $$L = \pi r$$ where $r$ is the radius. - Diameter $d$ relates to radius by $r = \frac{d}{2}$. - Perimeter of the shaded region will be the sum of the outer arcs plus the straight edges. 3. **Calculations:** (i) Large semi-circle radius $r = 7$ cm. $$\text{Arc length} = \pi \times 7 = 7\pi \text{ cm}$$ (ii) Smaller semi-circle diameter $d = 7$ cm, so radius $r = \frac{7}{2} = 3.5$ cm. $$\text{Arc length} = \pi \times 3.5 = 3.5\pi \text{ cm}$$ (iii) Perimeter of shaded region: - The shaded region consists of the large semi-circle minus the smaller semi-circle cut out, plus the smaller semi-circle reattached on the right. - The perimeter includes: - The arc of the large semi-circle: $7\pi$ - The arc of the smaller semi-circle: $3.5\pi$ - The straight line at the base of the large semi-circle: diameter $= 14$ cm - The straight line at the base of the smaller semi-circle is inside the large base, so it does not add to the perimeter. Therefore, total perimeter: $$P = 7\pi + 3.5\pi + 14 = 10.5\pi + 14 \text{ cm}$$ 4. **Final answers:** (i) $7\pi$ cm (ii) $3.5\pi$ cm (iii) $10.5\pi + 14$ cm