To calculate the total surface area of the truck, we need to find the surface area of both the cab and the cargo sections separately and then combine them.
Dimensions:
-
Cab Section (Left Prism):
- Height (h₁) = 3 inches
- Length (l₁) = 2 inches
- Depth (d₁) = visible depth, which we can infer from the total length and the dimensions of the cargo section.
-
Cargo Section (Right Prism):
- Height (h₂) = 6 inches
- The total length of the truck is 11 inches, so for the cargo section:
- Length (l₂) = 11 in (total length) - 2 in (length of cab) = 9 inches
- Depth (d₂) = 3 inches (given back depth)
Surface Area Calculation:
Surface Area of a Rectangular Prism: The formula for the surface area (SA) of a rectangular prism is: \[ SA = 2(lb + lh + bh) \] where \(l\) is the length, \(b\) is the breadth (or width), and \(h\) is the height.
1. Surface Area of the Cab Section:
- Length \(l₁ = 2\) in
- Width (assuming depth is the same as cargo, as both are truck surfaces) \(d₁ = d₂ = 3\) in (using the depth of the cargo)
- Height \(h₁ = 3\) in
Calculating the surface area: \[ SA_{cab} = 2(2 \cdot 3 + 2 \cdot 3 + 3 \cdot 3) = 2(6 + 6 + 9) = 2(21) = 42 \text{ in}² \]
2. Surface Area of the Cargo Section:
- Length \(l₂ = 9\) in
- Width \(d₂ = 3\) in
- Height \(h₂ = 6\) in
Calculating the surface area: \[ SA_{cargo} = 2(9 \cdot 3 + 9 \cdot 6 + 3 \cdot 6) = 2(27 + 54 + 18) = 2(99) = 198 \text{ in}² \]
Total Surface Area: Combining both sections: \[ SA_{total} = SA_{cab} + SA_{cargo} = 42 + 198 = 240 \text{ in}² \]
Conclusion:
This result does not match any of the provided options, suggesting there may be an alternative calculation housing error or the options might not represent the truck precisely.
If excluding the bottom surface of both prisms (if both are on wheels), the bottom surfaces would be as follows:
- Area of cab's base: \(l₁ \cdot d₁ = 2 \cdot 3 = 6 \text{ in}²\)
- Area of cargo's base: \(l₂ \cdot d₂ = 9 \cdot 3 = 27 \text{ in}²\)
Total areas of both bottoms: \(6 + 27 = 33 \text{ in}²\)
Subtracting from the total previously found: \[ SA_{final} = 240 - 33 = 207 \text{ in}² \]
This still misses given responses. A further review may be necessary for full alignment with options provided, such as checking the height assignment and compliance with the truck sitcom. Any misinterpretation here could lean towards more manual investigations into component separation or aggregation sensitivity.