To find the surface area of a rectangular prism, we use the formula:
[tex]\[ 2 \cdot ( \text{length} \cdot \text{width} ) + 2 \cdot ( \text{length} \cdot \text{height} ) + 2 \cdot ( \text{width} \cdot \text{height} ) \][/tex]
Given dimensions:
- Length ([tex]\( l \)[/tex]) = 5 inches
- Width ([tex]\( w \)[/tex]) = 3 inches
- Height ([tex]\( h \)[/tex]) = 8 inches
Let's break down the calculation step-by-step:
1. Calculate the area of the pairs of rectangular sides:
[tex]\[ \text{First pair of opposite sides: } 2 \cdot ( l \cdot w ) \][/tex]
[tex]\[ 2 \cdot ( 5 \cdot 3 ) = 2 \cdot 15 = 30 \text{ square inches} \][/tex]
[tex]\[ \text{Second pair of opposite sides: } 2 \cdot ( l \cdot h ) \][/tex]
[tex]\[ 2 \cdot ( 5 \cdot 8 ) = 2 \cdot 40 = 80 \text{ square inches} \][/tex]
[tex]\[ \text{Third pair of opposite sides: } 2 \cdot ( w \cdot h ) \][/tex]
[tex]\[ 2 \cdot ( 3 \cdot 8 ) = 2 \cdot 24 = 48 \text{ square inches} \][/tex]
2. Add the areas of all three pairs of opposite sides together:
[tex]\[ \text{Total Surface Area} = 30 \text{ square inches} + 80 \text{ square inches} + 48 \text{ square inches} \][/tex]
[tex]\[ \text{Total Surface Area} = 158 \text{ square inches} \][/tex]
Thus, the surface area of the rectangular prism is [tex]\(\boxed{158}\)[/tex] square inches.
Looking at the multiple-choice options, the correct answer is:
[tex]\[ \text{158} \][/tex]
