Question

select the correct answer.
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. $17.5\\ \text{ft}^2$

b. $41.5\\ \text{ft}^2$

c. $34.5\\ \text{ft}^2$

d. $36.5\\ \text{ft}^2$

Explanation:

Step1: Recall the surface area formula for a rectangular prism with a closed top.

The formula for the surface area \( S \) of a rectangular prism is \( S = 2(lw + lh + wh) \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Identify the given values.

We are given \( l = 3.5 \) feet, \( w = 2 \) feet, and \( h = 2.5 \) feet.

Step3: Substitute the values into the formula.

First, calculate \( lw \), \( lh \), and \( wh \):

• \( lw = 3.5\times2 = 7 \)
• \( lh = 3.5\times2.5 = 8.75 \)
• \( wh = 2\times2.5 = 5 \)

Then, substitute these into the surface area formula:
\( S = 2(7 + 8.75 + 5) \)

Step4: Simplify the expression inside the parentheses.

\( 7 + 8.75 + 5 = 20.75 \)

Step5: Multiply by 2.

\( S = 2\times20.75 = 41.5 \) square feet.

Answer:

B. \( 41.5\ \text{ft}^2 \)