1. **State the problem:** We have a circle with radius 4.57 m and a sector inside it defined by angle $\angle AOC = 2.17$ radians and radius $AO = OC = 3.36$ m. We need to find the area inside the circle that is not painted, i.e., the area of the circle minus the area of the painted sector. 2. **Formulas and rules:** - Area of a circle: $$A_{circle} = \pi r^2$$ - Area of a sector: $$A_{sector} = \frac{1}{2} r^2 \theta$$ where $r$ is the radius of the sector and $\theta$ is the central angle in radians. 3. **Calculate the area of the whole circle:** $$A_{circle} = \pi \times 4.57^2 = \pi \times 20.8849 = 65.60 \text{ m}^2 \text{ (approx)}$$ 4. **Calculate the area of the painted sector:** $$A_{sector} = \frac{1}{2} \times 3.36^2 \times 2.17 = \frac{1}{2} \times 11.2896 \times 2.17 = 12.25 \text{ m}^2 \text{ (approx)}$$ 5. **Calculate the unpainted area:** $$A_{unpainted} = A_{circle} - A_{sector} = 65.60 - 12.25 = 53.35 \text{ m}^2$$ 6. **Round to the nearest square metre:** $$\boxed{53 \text{ m}^2}$$ This is the area inside the circle that has not been painted.