To find the area of the base of the rectangular prism, follow these steps:
1. Determine the volume in cubic inches:
- First, note that the volume of the rectangular prism is given in cubic feet, which is 2.5 cubic feet.
- We need to convert this volume into cubic inches.
- From the unit conversion table, [tex]\(1 \text{ cubic foot} = 1728 \text{ cubic inches}\)[/tex].
- Multiply the volume in cubic feet by this conversion factor:
[tex]\[
2.5 \text{ cubic feet} \times 1728 \text{ cubic inches per cubic foot} = 4320 \text{ cubic inches}
\][/tex]
2. Use the volume formula for a rectangular prism:
- The volume [tex]\(V\)[/tex] of a rectangular prism can be expressed as the product of its base area [tex]\(A\)[/tex] and its height [tex]\(h\)[/tex], i.e.,
[tex]\[
V = A \times h
\][/tex]
- We need to find the base area [tex]\(A\)[/tex].
- We have the volume [tex]\(V = 4320 \text{ cubic inches}\)[/tex] and the height [tex]\(h = 15 \text{ inches}\)[/tex].
3. Solve for the base area:
- Rearrange the volume formula to solve for the base area [tex]\(A\)[/tex]:
[tex]\[
A = \frac{V}{h} = \frac{4320 \text{ cubic inches}}{15 \text{ inches}} = 288 \text{ square inches}
\][/tex]
Thus, the area of the base of the rectangular prism is [tex]\(\boxed{288} \text{ square inches}\)[/tex].
