Question

A carry-on suitcase is 9.6 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase?

(1 point)

96 in .^ 2

1, 451.5 in .^ 2

3, 420 in .^ 2

725.75 in .^ 2

Answer 1

To find the surface area of a rectangular suitcase, we use the formula for the surface area \( S \) of a rectangular prism:

\[
S = 2(lw + lh + wh)
\]

where \( l \), \( w \), and \( h \) are the length, width, and height of the suitcase, respectively.

Given:
- Length \( l = 9.6 \) inches
- Width \( w = 16 \) inches
- Height \( h = 22.5 \) inches

Now, we can calculate each of the areas:

1. \( lw = 9.6 \times 16 = 153.6 \)
2. \( lh = 9.6 \times 22.5 = 216 \)
3. \( wh = 16 \times 22.5 = 360 \)

Now, sum these areas together:

\[
lw + lh + wh = 153.6 + 216 + 360 = 729.6
\]

Now we can calculate the total surface area by multiplying by 2:

\[
S = 2 \times 729.6 = 1459.2 \text{ in}^2
\]

The surface area of the suitcase is approximately \( 1459.2 \) in\(^2\). This does not directly match the listed options, which makes it critical to examine our calculations. Reviewing them can show that:

- We likely made a minor mistake in the options rounding or calculation, which can frequently occur.
- The closest available option is **1,451.5 in.\(^2\)**.

Thus, the answer that best fits considering practical options available is **1,451.5 in.\(^2\)**.