SAT（英文）数学题求解.附解释 The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surfac

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SAT（英文）数学题求解.附解释 The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surfac
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SAT（英文）数学题求解.附解释 The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surfac
SAT（英文）数学题求解.附解释

 The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surface area of the large brick?

A. 32 

B. 40 

C. 60 

D. 72 

E. 80

SAT（英文）数学题求解.附解释 The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surfac
大砖的三个边长分别为a = 3,b = 2,c = 2(共3*2*2 = 12块小砖),表面积为2(ab + ac + bc) =2(3*2+3*2+2*2) = 32
每块小砖的表面积为6 (6个为边长为1的正方形),共为6*12 = 72
差:72 - 32 = 40
B

图中大的实心砖是由边长为一的小转拼成的。当把大砖拆分成小砖、所有小砖的总的表面积比大转的表面积大多少？
答案：B
大砖便面积=6×4+4×2=32
所有小砖总表面积=12×6=72
做差即可。

  1. 多出来的表面积是被覆盖在内部的面积，每个小正方体面积是6，

  2. 八的顶点位置没有漏出来的有三个这一部分增加的表面积是8*3=24

  3. 中间四个没有漏出来的面各有四个，这一部分增加的表面积是4*4=16

  4. 总共增加的表面积是40

    说的明白了没有，若是没有可以继续追问，明白了还想楼主采纳<...

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    1. 多出来的表面积是被覆盖在内部的面积，每个小正方体面积是6，

    2. 八的顶点位置没有漏出来的有三个这一部分增加的表面积是8*3=24

    3. 中间四个没有漏出来的面各有四个，这一部分增加的表面积是4*4=16

    4. 总共增加的表面积是40

      说的明白了没有，若是没有可以继续追问，明白了还想楼主采纳

    收起

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