To solve for the surface area of a rectangular prism, we need to use the surface area formula for a rectangular prism:
[tex]\[ \text{Surface Area} = 2 \times (lw + wh + hl) \][/tex]
where:
- [tex]\( l \)[/tex] is the length
- [tex]\( w \)[/tex] is the width
- [tex]\( h \)[/tex] is the height
Given:
- Length ([tex]\( l \)[/tex]) = 610 cm
- Width ([tex]\( w \)[/tex]) = 315 cm
- Height ([tex]\( h \)[/tex]) = 370 cm
Let's break it down step by step:
1. Calculate the area of each pair of faces:
- The area of the face with dimensions [tex]\( l \)[/tex] and [tex]\( w \)[/tex]: [tex]\( lw = 610 \, \text{cm} \times 315 \, \text{cm} \)[/tex]
- The area of the face with dimensions [tex]\( w \)[/tex] and [tex]\( h \)[/tex]: [tex]\( wh = 315 \, \text{cm} \times 370 \, \text{cm} \)[/tex]
- The area of the face with dimensions [tex]\( h \)[/tex] and [tex]\( l \)[/tex]: [tex]\( hl = 370 \, \text{cm} \times 610 \, \text{cm} \)[/tex]
2. Perform the calculations for each pair:
- [tex]\( lw = 192150 \, \text{cm}^2 \)[/tex]
- [tex]\( wh = 116550 \, \text{cm}^2 \)[/tex]
- [tex]\( hl = 225700 \, \text{cm}^2 \)[/tex]
3. Sum these three areas:
[tex]\[ lw + wh + hl = 192150 + 116550 + 225700 = 534400 \, \text{cm}^2 \][/tex]
4. Multiply the sum by 2 (since each pair of dimensions appears twice on the prism):
[tex]\[ \text{Surface Area} = 2 \times 534400 = 1068800 \, \text{cm}^2 \][/tex]
Now, we compare this result to the given options:
- Option 1: [tex]\( 30 \times 10^3 = 30000 \, \text{cm}^2 \)[/tex]
- Option 2: [tex]\( 5.34 \times 10^5 = 534000 \, \text{cm}^2 \)[/tex]
- Option 3: [tex]\( 1.07 \times 10^6 = 1070000 \, \text{cm}^2 \)[/tex]
- Option 4: [tex]\( 7.11 \times 10^7 = 71100000 \, \text{cm}^2 \)[/tex]
The correct answer that matches the computed surface area of 1068800 cm² is:
Option 3: [tex]\( 1.07 \times 10^6 \, \text{cm}^2 \)[/tex]
