To determine the amount of warehouse space needed for 430 boxes with each box having dimensions 13 inches by 6 inches by 11 inches, we can follow these steps:
1. Calculate the volume of one box in cubic inches:
- Given dimensions:
- Length = 13 inches
- Width = 6 inches
- Height = 11 inches
- Volume of one box in cubic inches [tex]\(V_{\text{in}} = \text{Length} \times \text{Width} \times \text{Height}\)[/tex]
- [tex]\(V_{\text{in}} = 13 \, \text{in} \times 6 \, \text{in} \times 11 \, \text{in}\)[/tex]
- [tex]\(V_{\text{in}} = 858 \, \text{cubic inches}\)[/tex]
2. Convert the volume of one box to cubic feet:
- There are [tex]\(12^3 = 1728\)[/tex] cubic inches in one cubic foot.
- Volume of one box in cubic feet [tex]\(V_{\text{ft}} = \frac{V_{\text{in}}}{1728}\)[/tex]
- [tex]\(V_{\text{ft}} = \frac{858 \, \text{cubic inches}}{1728}\)[/tex]
- [tex]\(V_{\text{ft}} = 0.4965277777777778 \, \text{cubic feet}\)[/tex]
3. Calculate the total warehouse space needed for 430 boxes:
- Total volume in cubic feet [tex]\(V_{\text{total}} = V_{\text{ft}} \times \text{Number of boxes}\)[/tex]
- [tex]\(V_{\text{total}} = 0.4965277777777778 \, \text{cubic feet} \times 430\)[/tex]
- [tex]\(V_{\text{total}} = 213.50694444444446 \, \text{cubic feet}\)[/tex]
4. Round the answer to the nearest tenth:
- [tex]\(V_{\text{total}} = 213.5 \, \text{cubic feet}\)[/tex]
Therefore, the amount of warehouse space needed for 430 boxes is 213.5 cubic feet.
