To find the approximate total surface area of the truck and its bed, we need to calculate the surface area of both rectangular prisms (the cab section and the cargo section) and then combine the results.
-
Cab Section:
- Dimensions:
- Length (L) = 4 feet
- Width (W) = Depth (D) = 7.5 feet (depth is given as 7.5 feet)
- Height (H) = 4 feet
- Surface Area (SA) of a rectangular prism is given by the formula: \[ SA = 2(LW + LH + WH) \]
- Plugging in the values for the cab section: \[ SA_{\text{cab}} = 2(4 \cdot 7.5 + 4 \cdot 4 + 7.5 \cdot 4) \] \[ = 2(30 + 16 + 30) = 2(76) \] \[ = 152 \text{ ft}^2 \]
- Dimensions:
-
Cargo Section:
- Dimensions:
- Length (L) = 15 feet
- Width (W) = 7.5 feet
- Height (H) = 7.5 feet
- Surface Area of the cargo section is calculated similarly: \[ SA_{\text{cargo}} = 2(15 \cdot 7.5 + 15 \cdot 7.5 + 7.5 \cdot 7.5) \] \[ = 2(112.5 + 112.5 + 56.25) = 2(281.25) \] \[ = 562.5 \text{ ft}^2 \]
- Dimensions:
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Total Surface Area:
- Combining both surface areas: \[ SA_{\text{total}} = SA_{\text{cab}} + SA_{\text{cargo}} \] \[ = 152 + 562.5 = 714.5 \text{ ft}^2 \]
Therefore, the approximate total surface area of the truck and its bed is 714.5 ft².
The correct response from the provided options is 714.5 ft.².