1. **State the problem:** We have two rectangular prisms (crates) with given dimensions and need to find the volume of the first and the height of the second. 2. **Recall the formula for volume of a rectangular prism:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 3. **Part (a): Find the volume of the first crate.** - Given: length = 3 ft, width = $2 \frac{1}{4} = \frac{9}{4}$ ft, height = 4 ft. - Calculate volume: $$V = 3 \times \frac{9}{4} \times 4$$ - Simplify step-by-step: $$V = 3 \times \frac{9}{\cancel{4}} \times \cancel{4} = 3 \times 9 = 27$$ - So, volume = 27 ft³. 4. **Part (b): Find the height of the second crate.** - Given: volume = 63 ft³, base area = $12 \frac{3}{5} = \frac{63}{5}$ ft². - Use formula: $$\text{Volume} = \text{Base Area} \times \text{Height}$$ - Solve for height: $$\text{Height} = \frac{\text{Volume}}{\text{Base Area}} = \frac{63}{\frac{63}{5}}$$ - Simplify: $$\text{Height} = 63 \times \frac{5}{63} = \cancel{63} \times \frac{5}{\cancel{63}} = 5$$ - So, height = 5 ft. **Final answers:** - (a) Volume = 27 ft³ - (b) Height = 5 ft