To find the surface area of a box, we will use the formula for the surface area of a rectangular prism:
[tex]\[ \text{Surface Area} = 2lw + 2lh + 2wh \][/tex]
Where:
- [tex]\( l \)[/tex] is the length (12 inches)
- [tex]\( w \)[/tex] is the width (8 inches)
- [tex]\( h \)[/tex] is the height (9 inches)
Step-by-step calculations:
1. Calculate the area of the three pairs of surfaces:
- The area of the top and bottom surfaces (length width) is:
[tex]\[ l \times w = 12 \times 8 = 96 \][/tex]
Therefore, two such surfaces together have an area of:
[tex]\[ 2 \times 96 = 192 \][/tex]
2. The area of the front and back surfaces (length height) is:
[tex]\[ l \times h = 12 \times 9 = 108 \][/tex]
Therefore, two such surfaces together have an area of:
[tex]\[ 2 \times 108 = 216 \][/tex]
3. The area of the left and right surfaces (width * height) is:
[tex]\[ w \times h = 8 \times 9 = 72 \][/tex]
Therefore, two such surfaces together have an area of:
[tex]\[ 2 \times 72 = 144 \][/tex]
4. Sum up the areas of all the surfaces:
[tex]\[ 192 + 216 + 144 = 552 \][/tex]
Therefore, the surface area of the box is 552 square inches.
From the given options:
A) 276 sq. in.
B) 444 sq. in.
C) 456 sq. in.
D) 552 sq. in.
The correct answer is:
D) 552 sq. in.
