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The solid brick shown is made of small bricks of side 1. When the larg

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The solid brick shown is made of small bricks of side 1. When the larg [#permalink]

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New post 12 May 2016, 01:48
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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

[Reveal] Spoiler:
Attachment:
2016-05-12_1244.png
2016-05-12_1244.png [ 1.52 KiB | Viewed 2963 times ]
[Reveal] Spoiler: OA

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Re: The solid brick shown is made of small bricks of side 1. When the larg [#permalink]

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New post 12 May 2016, 04:08
From the figure: The large brick is made up of 12 cubes.
Length of the large brick = 3
Width of large brick = 2
Height of large brick = 2

Total Surface area of the large brick = Total Surface area of a Cuboid = 2(3 * 2 + 2 * 2 + 3 * 2) = 2 * 16 = 32

Total Surface area of all 12 smaller bricks = 12 * (6 * 1) = 72

TSA of all small bricks - TSA of large brick = 72 - 32 = 40

Answer: B
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Re: The solid brick shown is made of small bricks of side 1. When the larg [#permalink]

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New post 12 May 2016, 06:54
Surface area of 12 single bricks
12*6*1^2 (Surface area of a cube is 6L^2)= 72

Surface area of large brick 2(3*2+3*2+2*2)= 32 (Surface area of rectangular solid is 2(LB+BL+HB) )

Difference will be 72-32= 40
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Re: The solid brick shown is made of small bricks of side 1. When the larg [#permalink]

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New post 10 Apr 2018, 17:22
Expert's post
Bunuel wrote:
Image
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

[Reveal] Spoiler:
Attachment:
2016-05-12_1244.png


The surface area of the large brick is composed of :

2(3 x 2) + 2(2 x 2) + 2(3 x 2) = 12 + 8 + 12 = 32

When the large brick is disassembled into small bricks of side 1, it can be disassembled into 3 x 2 x 2 = 12 small bricks. Since the surface area of each small brick is 6 x 1^2 = 6, the total surface area of the 12 small bricks is 6 x 12 = 72. Thus the total surface area of all the small bricks is 72 - 32 = 40 greater than the surface area of the large brick.

Answer: B
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Re: The solid brick shown is made of small bricks of side 1. When the larg   [#permalink] 10 Apr 2018, 17:22
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