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

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Joined: 02 Sep 2009
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The solid brick shown is made of small bricks of side 1. When the larg  [#permalink]

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12 May 2016, 01:48
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Difficulty:

35% (medium)

Question Stats:

75% (02:11) correct 25% (02:11) wrong based on 72 sessions

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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

Attachment:

2016-05-12_1244.png [ 1.52 KiB | Viewed 5865 times ]

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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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12 May 2016, 04:08
1
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

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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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12 May 2016, 06:54
2
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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10 Apr 2018, 17:22
Bunuel wrote:

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

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.

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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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24 May 2019, 18:10
Bunuel wrote:

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

Attachment:
2016-05-12_1244.png

Surface area of a cuboid (a,b,c) is 2*(ab+bc+ca)

Required-> Individual cubes SA - Big Cube SA
=> 12{2 (1+1+1)} - 2(3*2 + 2*2 + 2*3)
=40 (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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04 Jun 2019, 08:32
This is a fairly easy question on mensuration where you need to know the formula for the surface areas of a cuboid and a cube.

From the first statement of the question, we can make out that each brick is a cube of side 1.

The surface area of a cube of side ‘a’ is 6$$a^2$$. Therefore, the surface area of one brick is going to be 6 square units.

The surface area of a cuboid of length l, breadth b and height h is 2(lb + bh + lh). The length of the given cuboid is 3, the breadth 2 and the height 2. So, the surface area of the given cuboid (solid brick) is 2(6 + 4 + 6) = 32 sq units.

From the above, we can also calculate that there are a total of 12 bricks. The total surface area of the 12 bricks will therefore be 72 sq.units.
The difference between these two is 40 sq.units.

The correct answer option, therefore, is B.

Hope this helps!
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Re: The solid brick shown is made of small bricks of side 1. When the larg   [#permalink] 04 Jun 2019, 08:32
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