To determine the surface area of the box with dimensions 8 inches in width, 12 inches in length, and 9 inches in height, let's go through the problem step-by-step.
1. Identify the dimensions and formulas:
- Width ([tex]\( w \)[/tex]) = 8 inches
- Length ([tex]\( l \)[/tex]) = 12 inches
- Height ([tex]\( h \)[/tex]) = 9 inches
- The formula for the surface area ([tex]\( A \)[/tex]) of a rectangular box is:
[tex]\[ A = 2(lw + lh + wh) \][/tex]
2. Calculate the areas of each pair of opposite faces:
- Calculate the area of the face with dimensions [tex]\( l \)[/tex] and [tex]\( w \)[/tex]:
[tex]\[ lw = 12 \times 8 = 96 \text{ square inches} \][/tex]
- Calculate the area of the face with dimensions [tex]\( l \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ lh = 12 \times 9 = 108 \text{ square inches} \][/tex]
- Calculate the area of the face with dimensions [tex]\( w \)[/tex] and [tex]\( h \)[/tex]:
[tex]\[ wh = 8 \times 9 = 72 \text{ square inches} \][/tex]
3. Sum the calculated areas:
- The total surface area of the box is twice the sum of these areas:
[tex]\[ A = 2(lw + lh + wh) = 2(96 + 108 + 72) \][/tex]
4. Perform the final calculation:
[tex]\[ A = 2(96 + 108 + 72) = 2 \times 276 = 552 \text{ square inches} \][/tex]
Therefore, the approximate surface area of the box is:
[tex]\[ \boxed{552 \text{ square inches}} \][/tex]
Hence, the correct answer is:
D 552 sq. in.
