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.