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A storage bin is built as a rectangular prism with a closed top. The length is 3.5 feet, the width is 2 feet, and the height is 2.5 feet.

What is the amount of material needed to make the box?

A. [tex][tex]$34.5 \, \text{ft}^2$[/tex][/tex]
B. [tex][tex]$36.5 \, \text{ft}^2$[/tex][/tex]
C. [tex][tex]$41.5 \, \text{ft}^2$[/tex][/tex]
D. [tex][tex]$17.5 \, \text{ft}^2$[/tex][/tex]

Sagot :

GinnyAnswer
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]
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