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A rectangular solid brick of iron is melted and shaped into a cube. If

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Director
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A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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New post 15 Jul 2019, 09:19
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A rectangular solid brick of iron is melted and shaped into a cube. If the areas of different sides of the brick were 24, 36 and 54 square units respectively, what is the surface area of the cube in square units?

A. 36
B. 156
C. 216
D. 432
E. 2592
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Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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New post 15 Jul 2019, 11:11
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According to the information given let us suppose:

l*b=24
b*h=36
h*l=54

l/h=2/3 and b/l=2/3 so to get a ratio of l/b/h we have to get l at a common platform. l/h= 6/9 and b/l=4/6

now we can say l=6x, b=4x and h=9x

6x*4x=24
x=1
hence l=6, b=4, h=9

Volume of cuboid is 6*4*9
Volume of cuboid=Volume of cube

a3= 216
a=6

Surface Area of cube= 6a2
6*36= 216

Ans 216

Please Correct OA Bunuel
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Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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New post 15 Jul 2019, 21:56
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mangamma wrote:
A rectangular solid brick of iron is melted and shaped into a cube. If the areas of different sides of the brick were 24, 36 and 54 square units respectively, what is the surface area of the cube in square units?

A. 36
B. 156
C. 216
D. 432
E. 2592


Say the dimensions of the rectangular solid brick were x, y, and z.
xy = 24
xz = 36
yx = 54

Multiply all three: (xyz)^2 = 24*36*54 =(3*8)*36*(2*3^3) = 16*3^4*36

xyz = the volume of the rectangular solid brick = \(\sqrt{16*3^4*36} = 4*3^2*6=216\).

The volume of the rectangular solid brick = the volume of the cube = 216.

Thus, the edge of the cube = \(\sqrt[3]{216}=6\).

The surface area of the cube = (are of a face)*(number of faces) = 6^2*6 = 216.

Answer: C.
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Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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New post 02 Jul 2020, 06:46
vol of brick = vol of cube

let
lb = 24
bh = 36
hb = 54

(lbh)^2 = 24*54*36
(lbh)^2 = 3^6*2^6
lbh = 6^3
vol of cube = a^3
a = 6

to find surface area = 6a^2 = 6^3 = 216
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Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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New post 02 Jul 2020, 06:58
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Please refer to the pic uploaded

IMO ans is C.

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Re: A rectangular solid brick of iron is melted and shaped into a cube. If   [#permalink] 02 Jul 2020, 06:58

A rectangular solid brick of iron is melted and shaped into a cube. If

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