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The figure shown is composed of 4 identical cubes. Find the surface area. The surface area of the figure is _____ in².

The figure shown is composed of 4 identical cubes. Find the surface area. The surface area of the figure is _____ in.².




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1 Answer

  1. To find the surface area of the figure composed of 4 identical cubes, we first determine the surface area of one cube and then account for the configuration of the cubes.

    1. Surface Area of One Cube: The surface area (SA) of a single cube is given by the formula:

    [

    SA = 6a^2

    ]

    where (a) is the length of one edge of the cube.

    2. Configuration: When cubes are combined, the surfaces that touch each other do not contribute to the outside surface area. So, we need to visualize how the cubes are arranged.

    Assuming they are arranged such that some faces are touching, we will need to subtract the areas of the contact faces from the total surface area.

    3. Calculation: Without specific dimensions or arrangement of the cubes, I can’t provide an exact number. However, in a typical arrangement of 4 cubes (like a 2×2 layout), you might see 2 faces of each cube touching another, which would reduce the exposed surface areas.

    For example, if each cube has an edge length of (a):

    – The total surface area of 4 cubes without any touching would be:

    [

    SA_{text{total}} = 4 times 6a^2 = 24a^2

    ]

    – Considering a 2×2 configuration would mean subtracting some shared face areas.

    Thus, the

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