1. **State the problem:** We need to estimate the number of vertical cross sections required so that their total area equals the area of the base of a rectangular prism with dimensions 8 cm by 6 cm. 2. **Identify the base area:** The base is a rectangle with length 8 cm and width 6 cm. 3. **Calculate the base area:** $$\text{Base area} = 8 \times 6 = 48 \text{ cm}^2$$ 4. **Understand vertical cross sections:** Vertical cross sections are slices perpendicular to the base, each with an area equal to the height times the width or length depending on orientation. 5. **Choose cross section orientation:** Assume vertical cross sections are taken parallel to the 6 cm side, so each cross section is a rectangle of height 3 cm and width 6 cm. 6. **Calculate area of one vertical cross section:** $$\text{Area per cross section} = 3 \times 6 = 18 \text{ cm}^2$$ 7. **Estimate number of cross sections needed:** $$\text{Number} = \frac{\text{Base area}}{\text{Area per cross section}} = \frac{48}{18} = \frac{\cancel{48}}{\cancel{18}} = \frac{16}{6} \approx 2.67$$ 8. **Round to nearest whole number:** 3 cross sections. 9. **Compare estimate to actual:** Since 2.67 is rounded up to 3, the estimate is slightly higher than the exact fractional number needed. **Final answer:** Approximately 3 vertical cross sections are needed, which is a slight overestimate compared to the exact value of about 2.67.