Mathematics

Question

A cube consists of twenty-seven 2×2×2
-inch small cubes. All four of the corner cubes on the edge of the top layer fell off. Which statement is true about the surface area of the resulting solid?
ANSWER FAST!!

2 Answer

  • The answer is that it is the same surface area of the original cube
  • Answer:

    248 cubic inches

    Step-by-step explanation:

    The cube consists of twenty-seven 2×2×2-inch small cubes.

    So, there are three layers in the cube and each layer has 3 rows and 3 columns.

    So, the dimensions of the cube are:

    6 inches × 6 inches × 6 inches

    Hence, the surface area of the cube is 6[tex]a^{2}[/tex] = 6[tex](6^{2} )[/tex]

    = 216 cubic inches.

    If, all four of the corner cubes on the edge of the top layer fell off,

    then the surface area of the top layer is [tex]6^{2}[/tex] + sum of the side areas of the cubes adjacent to the removed cubes

    Note that if one corner cube is removed, then the areas of the sides of the adjacent two cubes should be calculated in the surface area calculation. Since, 4 cubes at the corners are removed, 4 × 2 = 8 faces' area to be calculated.

    Therefore,

    Surface area of the new cube = 5([tex]6^{2}[/tex]) + ([[tex]6^{2}[/tex] + 8(4)])

    = 5(36) + (36+32)

    = 180 + 68

    = 248 cubic inches

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