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. 36.5 ft² b. 41.5 ft² c. 34.5 ft² d. 17.5 ft²

Explanation:

Step1: Recall surface - area formula for rectangular prism

The surface - area formula of a rectangular prism with length $l$, width $w$, and height $h$ is $SA = 2(lw+lh + wh)$.

Step2: Substitute given values

Given $l = 3.5$ ft, $w = 2$ ft, and $h = 2.5$ ft.
First, calculate $lw$: $lw=3.5\times2 = 7$ ft².
Then, calculate $lh$: $lh = 3.5\times2.5=8.75$ ft².
Next, calculate $wh$: $wh=2\times2.5 = 5$ ft².

Step3: Calculate the sum inside the parentheses

$lw+lh + wh=7 + 8.75+5=20.75$ ft².

Step4: Multiply by 2

$SA = 2\times20.75 = 41.5$ ft².

Answer:

B. 41.5 ft²