1. **State the problem:** We have a rectangular pastry of width 37 cm and height 20 cm with eight circles cut out. Each circle has a diameter of 8 cm. We need to find the area of the pastry left after cutting out the circles, rounded to three significant figures. 2. **Formula for area of rectangle:** $$\text{Area}_{\text{rectangle}} = \text{width} \times \text{height}$$ 3. **Formula for area of a circle:** $$\text{Area}_{\text{circle}} = \pi r^2$$ where $r$ is the radius of the circle. 4. **Calculate the area of the rectangle:** $$37 \times 20 = 740 \text{ cm}^2$$ 5. **Calculate the radius of each circle:** Diameter = 8 cm, so radius $r = \frac{8}{2} = 4$ cm. 6. **Calculate the area of one circle:** $$\pi \times 4^2 = \pi \times 16 = 16\pi \text{ cm}^2$$ 7. **Calculate the total area of eight circles:** $$8 \times 16\pi = 128\pi \text{ cm}^2$$ 8. **Calculate the area of pastry left:** $$740 - 128\pi$$ 9. **Evaluate the numerical value:** Using $\pi \approx 3.1416$, $$128 \times 3.1416 = 402.123$$ 10. **Final area left:** $$740 - 402.123 = 337.877 \text{ cm}^2$$ Rounded to three significant figures: $$\boxed{338 \text{ cm}^2}$$