Question

A hot chocolate company is deciding which box shape to use for their new product line. The first box (Box A) measures 8 inches by 6 inches by 9 inches. The second box (Box B) measures 9 inches by 4 inches by 13 inches. Which box requires more material to make?(1 point)
Responses

Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 410 square inches.
Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 410 square inches.

Box A requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 205 square inches.
Box A requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 205 square inches.

Both Box A and Box B require the same amount of material.
Both Box A and Box B require the same amount of material.

Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 366 square inches.

Answer 1

To determine which box requires more material, we will calculate the surface area of both boxes.

**Surface Area Formula for a Rectangular Box:**
The surface area (SA) of a rectangular box can be calculated using the formula:
\[
SA = 2(lw + lh + wh)
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

### For Box A:
Dimensions: \( 8 \) inches (length) × \( 6 \) inches (width) × \( 9 \) inches (height).

\[
SA_A = 2(8 \times 6 + 8 \times 9 + 6 \times 9)
\]

Calculating each term:
- \( 8 \times 6 = 48 \)
- \( 8 \times 9 = 72 \)
- \( 6 \times 9 = 54 \)

Now substituting back into the surface area formula:
\[
SA_A = 2(48 + 72 + 54) = 2(174) = 348 \text{ square inches}
\]

### For Box B:
Dimensions: \( 9 \) inches (length) × \( 4 \) inches (width) × \( 13 \) inches (height).

\[
SA_B = 2(9 \times 4 + 9 \times 13 + 4 \times 13)
\]

Calculating each term:
- \( 9 \times 4 = 36 \)
- \( 9 \times 13 = 117 \)
- \( 4 \times 13 = 52 \)

Now substituting back into the surface area formula:
\[
SA_B = 2(36 + 117 + 52) = 2(205) = 410 \text{ square inches}
\]

### Conclusion:
- **Box A** requires **348 square inches** of material.
- **Box B** requires **410 square inches** of material.

Therefore, the correct response is:

**Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 410 square inches.**