1. **State the problem:** We need to find the volume of the frustum of a rectangular-based pyramid. The frustum is formed by cutting a larger pyramid horizontally, leaving a smaller pyramid on top and the frustum below. 2. **Given dimensions:** - Smaller pyramid height $h_1 = 9$ cm, base length $l_1 = 3$ cm, base width $w_1 = 6$ cm - Frustum height $h_f = 24$ cm, base length $l_f = 11$ cm, base width $w_f = 22$ cm 3. **Find the height of the original larger pyramid:** The frustum is the part left after cutting the smaller pyramid from the larger one. The total height $H$ of the original pyramid is the sum of the frustum height and the smaller pyramid height: $$H = h_f + h_1 = 24 + 9 = 33 \text{ cm}$$ 4. **Volume formula for a pyramid:** $$V = \frac{1}{3} \times \text{base area} \times \text{height}$$ 5. **Calculate the volume of the smaller pyramid:** Base area of smaller pyramid: $$A_1 = l_1 \times w_1 = 3 \times 6 = 18 \text{ cm}^2$$ Volume: $$V_1 = \frac{1}{3} \times 18 \times 9 = \frac{1}{3} \times 162 = 54 \text{ cm}^3$$ 6. **Calculate the volume of the larger pyramid:** Base area of larger pyramid: $$A_2 = l_f \times w_f = 11 \times 22 = 242 \text{ cm}^2$$ Volume: $$V_2 = \frac{1}{3} \times 242 \times 33 = \frac{1}{3} \times 7986 = 2662 \text{ cm}^3$$ 7. **Calculate the volume of the frustum:** The frustum volume is the volume of the larger pyramid minus the volume of the smaller pyramid: $$V_f = V_2 - V_1 = 2662 - 54 = 2608 \text{ cm}^3$$ **Final answer:** The volume of the frustum is $2608$ cubic centimeters.