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Part 1
Find the volume and surface area of the figure.
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Part 1
2 in
3 in
5.8 in
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Part 1
The volume of the figure is
  
enter your response here in cubed.

1 answer

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