1. **State the problem:** We have a prism with a square cross-section of side 13 cm and depth 5 cm. There is a circular hole through the prism with diameter 6 cm. We need to find the volume of the shape after the hole is removed. 2. **Formula for volume of prism:** $$V = \text{area of cross-section} \times \text{depth}$$ 3. **Calculate the volume of the full prism (without hole):** The cross-section is a square with side 13 cm, so area is: $$13 \times 13 = 169 \text{ cm}^2$$ Depth is 5 cm, so volume is: $$V_{prism} = 169 \times 5 = 845 \text{ cm}^3$$ 4. **Calculate the volume of the cylindrical hole:** The hole is a cylinder with diameter 6 cm, so radius $r = \frac{6}{2} = 3$ cm. The area of the circular cross-section is: $$\pi r^2 = \pi \times 3^2 = 9\pi \text{ cm}^2$$ The depth is the same 5 cm, so volume of hole is: $$V_{hole} = 9\pi \times 5 = 45\pi \text{ cm}^3$$ 5. **Calculate the volume of the shape with hole:** $$V = V_{prism} - V_{hole} = 845 - 45\pi$$ 6. **Evaluate numerically:** Using $\pi \approx 3.1416$, $$45\pi \approx 45 \times 3.1416 = 141.372$$ So, $$V \approx 845 - 141.372 = 703.628 \text{ cm}^3$$ 7. **Round to 3 significant figures:** $$\boxed{704 \text{ cm}^3}$$ This is the volume of the shape with the circular hole removed.