1. **Problem Statement:** Convert and calculate volumes using imperial units of volume and capacity. 2. **Formulas and Conversion Rules:** - 1 yard (yd) = 3 feet (ft) - 1 foot (ft) = 12 inches (in) - Volume conversions: $$1 \text{ yd}^3 = (3 \text{ ft})^3 = 27 \text{ ft}^3$$ $$1 \text{ ft}^3 = (12 \text{ in})^3 = 1728 \text{ in}^3$$ 3. **Conversions:** - Convert 4 yd³ to ft³: $$4 \text{ yd}^3 = 4 \times 27 = 108 \text{ ft}^3$$ - Convert 72 ft³ to yd³: $$72 \text{ ft}^3 = \frac{72}{27} = \frac{\cancel{72}}{\cancel{27}} = 2.6667 \text{ yd}^3$$ - Convert 3 ft³ to in³: $$3 \text{ ft}^3 = 3 \times 1728 = 5184 \text{ in}^3$$ - Convert $\frac{2}{3}$ yd³ to ft³ and in³: $$\frac{2}{3} \text{ yd}^3 = \frac{2}{3} \times 27 = 18 \text{ ft}^3$$ $$18 \text{ ft}^3 = 18 \times 1728 = 31104 \text{ in}^3$$ 4. **Word Problems:** **1a. Volume of tissue box in cubic inches:** $$V = \text{length} \times \text{width} \times \text{height} = 9 \times 5 \times 3 = 135 \text{ in}^3$$ **1b. Volume of tissue box in cubic feet:** $$135 \text{ in}^3 = \frac{135}{1728} = \frac{\cancel{135}}{\cancel{1728}} \approx 0.0781 \text{ ft}^3$$ **2. Volume of soil in cubic yards for 28 loads:** $$\text{Volume per load} = 2.5 \text{ ft}^3$$ $$\text{Total volume} = 28 \times 2.5 = 70 \text{ ft}^3$$ $$70 \text{ ft}^3 = \frac{70}{27} \approx 2.6 \text{ yd}^3$$ **3. Number of trips for cement delivery:** $$\text{Total cement} = 32 \text{ yd}^3 = 32 \times 27 = 864 \text{ ft}^3$$ $$\text{Truck capacity} = 216 \text{ ft}^3$$ $$\text{Number of trips} = \frac{864}{216} = 4$$ **Final answers:** - 4 yd³ = 108 ft³ - 72 ft³ = 2.67 yd³ - 3 ft³ = 5184 in³ - 2/3 yd³ = 18 ft³ = 31104 in³ - Tissue box volume: 135 in³ or 0.0781 ft³ - Soil volume in 28 loads: 2.6 yd³ - Cement delivery trips: 4