A carry-on suitcase is 9.5 inches long, 16 inches wide, and 22.5 inches high. What is the surface area of the suitcase?(1 point) Responses 3,420 in.2 3 comma 420 in. squared 725.75 in.2 725 point 7 5 in. squared 1,451.5 in.2 1 comma 451 point 5 in. squared 96 in.2

1 answer

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

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

where \(l\) is the length, \(w\) is the width, and \(h\) is the height.

Given:

  • Length \(l = 9.5\) inches
  • Width \(w = 16\) inches
  • Height \(h = 22.5\) inches

Now, calculate each of the areas:

  1. \(lw = 9.5 \times 16 = 152\) in²
  2. \(lh = 9.5 \times 22.5 = 213.75\) in²
  3. \(wh = 16 \times 22.5 = 360\) in²

Now, sum these areas:

\[ lw + lh + wh = 152 + 213.75 + 360 = 725.75 \text{ in}² \]

Finally, multiply this sum by 2 to find the total surface area:

\[ S = 2 \times 725.75 = 1451.5 \text{ in}² \]

Thus, the surface area of the suitcase is 1,451.5 in.².

The correct response is 1,451.5 in.².