Missy wants to find the surface area of a snack box in her pantry.

Question

A prism has a length of 3 inches, height of 10 inches, and width of 6 inches.

Her work is shown below.

Steps
Missy’s Work
Step 1
Front or back: 3 x 10 = 30
Left or right: 6 x 10 = 60
Top or bottom: 3 x 6 = 18
Step 2
30 + 60 + 18
Step 3
108 in.²

Where, if any, did Missy first make a mistake finding the surface area of the snack box?
Step 1: Missy did not calculate the area of the front or back sides correctly.
Step 1: Missy did not calculate the area of the left or right sides correctly.
Step 2: Missy did not multiply the area of each face by 2 before adding.
Step 2: Missy did not multiply the area of each face by 3 before adding.

Answer 1

Missy made a mistake in her Step 2. She did not multiply the area of each face by 2 before adding.

In a rectangular prism, each pair of opposite faces has the same area. Here's the correct breakdown:

1. Front or Back (2 faces): \(2 \times (3 \times 10) = 2 \times 30 = 60\) in²
2. Left or Right (2 faces): \(2 \times (6 \times 10) = 2 \times 60 = 120\) in²
3. Top or Bottom (2 faces): \(2 \times (3 \times 6) = 2 \times 18 = 36\) in²

Now, summing these areas gives:

\[ 60 + 120 + 36 = 216 \text{ in²} \]

Thus, the correct surface area is 216 in². Missy’s error was in not multiplying the area of each face by 2 before adding them together.