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When 88 cubes are rearranged to form the solid structure shown in the

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When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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New post 24 May 2019, 17:05
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A
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C
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E

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56% (02:17) correct 44% (01:13) wrong based on 9 sessions

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When 88 cubes are rearranged to form the solid structure shown in the diagram below, their total surface area decreases by 384 units. Find the total surface area of the solid structure.

A. 96
B. 128
C. 144
D. 160
E. 176

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Re: When 88 cubes are rearranged to form the solid structure shown in the  [#permalink]

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New post 24 May 2019, 20:22
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nick1816 wrote:
When 88 cubes are rearranged to form the solid structure shown in the diagram below, their total surface area decreases by 384 units. Find the total surface area of the solid structure.

A. 96
B. 128
C. 144
D. 160
E. 176




Here is my approach to the above problem.

Surface area of a cube is 6*(x^2) where x is the length of the cube.

Now,

Surface area of 88 cubes before they form the solid structure = 88 * 6 * x^2= 528* (x^2)


Surface area of the solid structure =

Surface area of each face of solid structure = 16 small cubes with one face exposed (4 hidden are further compensated in the structure that is overlaying)+ 8 side faces of each structure overlaying (more like walls supporting them) = 24 cubes with only one side exposed.

We know total faces of a cube is 6 .So total Surface area of solid structure = 24* 6* x^2 = 144 *x^2


Now from question

When 88 cubes are rearranged to form the solid structure shown in the diagram below, their total surface area decreases by 384 units.

Implies

528* (x^2) - 144 *x^2= 384

384*(x^2) =384

x = 1


Therefore total surface area of solid structure = 144 *x^2 = 144

So I guess C should be the option.



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Re: When 88 cubes are rearranged to form the solid structure shown in the   [#permalink] 24 May 2019, 20:22
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When 88 cubes are rearranged to form the solid structure shown in the

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