To find the volume and surface area of the given figure, we first need to identify the shape based on its dimensions 2, 6, and 13. Given these values, it seems likely that the figure is a rectangular prism with the sides being 2 ft, 6 ft, and 13 ft.
1. Volume of the Rectangular Prism
The volume \( V \) of a rectangular prism is calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \]
Here, let's take:
- Length = 13 ft
- Width = 6 ft
- Height = 2 ft
Substituting the values: \[ V = 13 , \text{ft} \times 6 , \text{ft} \times 2 , \text{ft} \] \[ V = 156 , \text{ft}^3 \]
2. Surface Area of the Rectangular Prism
The surface area \( SA \) of a rectangular prism is given by the formula: \[ SA = 2(\text{length} \times \text{width} + \text{width} \times \text{height} + \text{height} \times \text{length}) \]
Plugging in our dimensions: \[ SA = 2(13 , \text{ft} \times 6 , \text{ft} + 6 , \text{ft} \times 2 , \text{ft} + 2 , \text{ft} \times 13 , \text{ft}) \]
Calculating each component:
- \( 13 \times 6 = 78 \)
- \( 6 \times 2 = 12 \)
- \( 2 \times 13 = 26 \)
Now substituting these into the surface area formula: \[ SA = 2(78 + 12 + 26) \] \[ SA = 2(116) \] \[ SA = 232 , \text{ft}^2 \]
Conclusion
Combining our results:
- Volume \( V = 156 , \text{ft}^3 \)
- Surface Area \( SA = 232 , \text{ft}^2 \)
Thus, the correct answer is: B. V = 156 ft³; SA = 232 ft²