To determine which box requires more material to make, we need to calculate the surface area of both Box A and Box B.
Box A dimensions: 8 inches × 6 inches × 9 inches
The surface area \( SA \) of a rectangular box can be calculated using the formula: \[ SA = 2(lw + lh + wh) \] where \( l \), \( w \), and \( h \) are the length, width, and height of the box.
For Box A: \[ l = 8, \quad w = 6, \quad h = 9 \] \[ SA_A = 2(8 \cdot 6 + 8 \cdot 9 + 6 \cdot 9) \] Calculating each term: \[ 8 \cdot 6 = 48 \] \[ 8 \cdot 9 = 72 \] \[ 6 \cdot 9 = 54 \] Now, adding those together: \[ 48 + 72 + 54 = 174 \] Then multiplying by 2: \[ SA_A = 2 \cdot 174 = 348 \text{ square inches} \]
Box B dimensions: 9 inches × 4 inches × 13 inches
For Box B: \[ l = 9, \quad w = 4, \quad h = 13 \] \[ SA_B = 2(9 \cdot 4 + 9 \cdot 13 + 4 \cdot 13) \] Calculating each term: \[ 9 \cdot 4 = 36 \] \[ 9 \cdot 13 = 117 \] \[ 4 \cdot 13 = 52 \] Now, adding those together: \[ 36 + 117 + 52 = 205 \] Then multiplying by 2: \[ SA_B = 2 \cdot 205 = 410 \text{ square inches} \]
Now we compare the surface areas:
- Box A = 348 square inches
- Box B = 410 square inches
Thus, Box B requires more material to make.
The correct answer 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.