1. **Problem 1: Work out the area of the shaded section when the radius of the circle is 7 cm.** 2. The shaded section is a quarter circle inside a square, so the area of the shaded section is the area of the quarter circle. 3. The formula for the area of a circle is $$A = \pi r^2$$. 4. Since the shaded section is a quarter of the circle, its area is $$\frac{1}{4} \pi r^2$$. 5. Substitute the radius $r = 7$ cm: $$\text{Area} = \frac{1}{4} \pi (7)^2 = \frac{1}{4} \pi 49 = \frac{49}{4} \pi$$ 6. Calculate the numerical value: $$\frac{49}{4} \pi \approx 12.25 \times 3.1416 = 38.48 \text{ cm}^2$$ --- 1. **Problem 2: How much longer is the big arc than the small arc?** 2. The length of an arc is given by the formula: $$L = r \theta$$ where $r$ is the radius and $\theta$ is the angle in radians. 3. Convert the angle from degrees to radians: $$\theta = 120^\circ = 120 \times \frac{\pi}{180} = \frac{2\pi}{3}$$ 4. Calculate the length of the big arc with radius 4 cm: $$L_{big} = 4 \times \frac{2\pi}{3} = \frac{8\pi}{3}$$ 5. Calculate the length of the small arc with radius 1 cm: $$L_{small} = 1 \times \frac{2\pi}{3} = \frac{2\pi}{3}$$ 6. Find the difference: $$L_{diff} = L_{big} - L_{small} = \frac{8\pi}{3} - \frac{2\pi}{3} = \frac{6\pi}{3} = 2\pi$$ 7. Calculate the numerical value: $$2\pi \approx 2 \times 3.1416 = 6.3 \text{ cm}$$ **Final answers:** - Area of shaded section: $38.48$ cm$^2$ - Difference in arc lengths: $6.3$ cm