To determine the amount of material needed to make the storage bin, we need to calculate the surface area of the rectangular prism. Here’s the step-by-step process to find the surface area:
1. Identify the dimensions of the rectangular prism:
- Length ([tex]\(l\)[/tex]) = 3.5 feet
- Width ([tex]\(w\)[/tex]) = 2 feet
- Height ([tex]\(h\)[/tex]) = 2.5 feet
2. Recall the surface area formula for a rectangular prism:
[tex]\[
\text{Surface Area} = 2(lw + lh + wh)
\][/tex]
3. Plug in the values:
- Calculate [tex]\(lw\)[/tex]:
[tex]\[
lw = 3.5 \text{ feet} \times 2 \text{ feet} = 7 \text{ ft}^2
\][/tex]
- Calculate [tex]\(lh\)[/tex]:
[tex]\[
lh = 3.5 \text{ feet} \times 2.5 \text{ feet} = 8.75 \text{ ft}^2
\][/tex]
- Calculate [tex]\(wh\)[/tex]:
[tex]\[
wh = 2 \text{ feet} \times 2.5 \text{ feet} = 5 \text{ ft}^2
\][/tex]
4. Sum these values:
[tex]\[
lw + lh + wh = 7 \text{ ft}^2 + 8.75 \text{ ft}^2 + 5 \text{ ft}^2 = 20.75 \text{ ft}^2
\][/tex]
5. Multiply the sum by 2 to get the total surface area:
[tex]\[
\text{Surface Area} = 2 \times 20.75 \text{ ft}^2 = 41.5 \text{ ft}^2
\][/tex]
Therefore, the amount of material needed to make the box is [tex]\(41.5 \text{ ft}^2\)[/tex].
The correct answer is:
C. [tex]\(41.5 \text{ ft}^2\)[/tex]
