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 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.

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.
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.

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.

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

Answer 1

To determine which box requires more material to make, we need to calculate the surface area of each box. The surface area \( S \) of a rectangular box can be calculated using the formula:

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

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

**For Box A (8 inches x 6 inches x 9 inches):**

- Length \( l = 8 \)
- Width \( w = 6 \)
- Height \( h = 9 \)

\[
S_A = 2(8 \cdot 6 + 8 \cdot 9 + 6 \cdot 9) = 2(48 + 72 + 54) = 2(174) = 348 \text{ square inches}
\]

**For Box B (9 inches x 4 inches x 13 inches):**

- Length \( l = 9 \)
- Width \( w = 4 \)
- Height \( h = 13 \)

\[
S_B = 2(9 \cdot 4 + 9 \cdot 13 + 4 \cdot 13) = 2(36 + 117 + 52) = 2(205) = 410 \text{ square inches}
\]

Now, comparing the surface areas:

- Box A: 348 square inches
- Box B: 410 square inches

Thus, **Box B requires more material to make** because:
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.