1. **Problem statement:** We need to find the volume of a frustum formed by removing a smaller rectangular-based pyramid from a larger similar pyramid. 2. **Given data:** - Larger pyramid base dimensions: 45 cm by 30 cm - Larger pyramid height: 10 cm - Smaller pyramid base dimensions: 6 cm by 6 cm - Smaller pyramid height: 10 cm 3. **Important note:** The smaller pyramid is similar to the larger one, so the ratio of corresponding linear dimensions is constant. 4. **Step 1: Calculate the volume of the larger pyramid.** The volume formula for a pyramid is: $$V = \frac{1}{3} \times \text{base area} \times \text{height}$$ Base area of larger pyramid: $$45 \times 30 = 1350 \text{ cm}^2$$ Volume of larger pyramid: $$V_{large} = \frac{1}{3} \times 1350 \times 10 = 4500 \text{ cm}^3$$ 5. **Step 2: Find the scale factor between the smaller and larger pyramid.** Since the pyramids are similar, the ratio of corresponding sides is the same. We can use the base lengths to find the scale factor $k$: $$k = \frac{6}{45} = \frac{2}{15}$$ 6. **Step 3: Calculate the height of the smaller pyramid using the scale factor.** Since the height scales the same way: $$h_{small} = k \times h_{large} = \frac{2}{15} \times 10 = \frac{20}{15} = \frac{4}{3} \approx 1.333 \text{ cm}$$ 7. **Step 4: Calculate the volume of the smaller pyramid.** Base area of smaller pyramid: $$6 \times 6 = 36 \text{ cm}^2$$ Volume of smaller pyramid: $$V_{small} = \frac{1}{3} \times 36 \times \frac{4}{3} = \frac{1}{3} \times 36 \times 1.333 = 16 \text{ cm}^3$$ 8. **Step 5: Calculate the volume of the frustum.** The frustum volume is the volume of the larger pyramid minus the volume of the smaller pyramid: $$V_{frustum} = V_{large} - V_{small} = 4500 - 16 = 4484 \text{ cm}^3$$ **Final answer:** The volume of the frustum is **4484 cm³**.