To find the volume and surface area of the figure, we need to know the type of figure you're asking about. The dimensions provided appear to indicate it may be a rectangular prism with dimensions of 2 inches, 3 inches, and 5.8 inches.
Volume:
The volume (\(V\)) of a rectangular prism can be calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \]
Using the dimensions you provided:
- length = 2 in
- width = 3 in
- height = 5.8 in
Calculating the volume: \[ V = 2 \text{ in} \times 3 \text{ in} \times 5.8 \text{ in} = 34.8 \text{ in}^3 \]
So, the volume of the figure is 34.8 cubic inches.
Surface Area:
The surface area (\(A\)) of a rectangular prism can be calculated using the formula: \[ A = 2(lw + lh + wh) \]
Where:
- \( l = 2 \text{ in} \)
- \( w = 3 \text{ in} \)
- \( h = 5.8 \text{ in} \)
Calculating each area component:
- \( lw = 2 \text{ in} \times 3 \text{ in} = 6 \text{ in}^2 \)
- \( lh = 2 \text{ in} \times 5.8 \text{ in} = 11.6 \text{ in}^2 \)
- \( wh = 3 \text{ in} \times 5.8 \text{ in} = 17.4 \text{ in}^2 \)
Now, substitute back into the surface area formula: \[ A = 2(6 + 11.6 + 17.4) = 2(35) = 70 \text{ in}^2 \]
So, the surface area of the figure is 70 square inches.
Final Answers:
- Volume: 34.8 in³
- Surface Area: 70 in²