Question

Three same-sized cubes are glued together as shown below.

If the side length of each cube is 6 inches, what is the surface area of the figure?

Answer 1

540

Step-by-step explanation:

The easiest way to do this is to:

Find the surface area of ONE cube minus a side

6*6= 36*5 = 180

Then multiply it by THREE to find the total surface area:

180*3 = 540

Answer 2

The surface area of the figure composed of three cubes each with a side length of 6 inches is 576 square inches, after accounting for the shared faces between the cubes.

Step-by-step explanation:

The surface area of a figure is the total area of all its outside surfaces. For a cube, this consists of 6 squares, and since each side of these cubes is 6 inches, the area of one face is 6*6 = 36 square inches.

However, in this case, we have three cubes stuck together. Assuming that they are stuck together face-to-face (flat side to flat side), some faces won't be visible anymore as they'll be shared between cubes. These invisible faces won't count towards the surface area. Typically, a single cube has 6 faces, so three cubes would initially have 18 faces (6 faces * 3). Assuming it forms a straight line, we would subtract 2 faces (one face from the middle cube for each side cube). Therefore 16 faces would be visible. So, the total surface area is 16 faces * 36 square inches/face = 576 square inches.

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