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

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Director
Joined: 25 Dec 2018
Posts: 651
Location: India
Concentration: General Management, Finance
GMAT Date: 02-18-2019
GPA: 3.4
WE: Engineering (Consulting)
A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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15 Jul 2019, 09:19
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Difficulty:

35% (medium)

Question Stats:

76% (02:08) correct 24% (02:18) wrong based on 90 sessions

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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
Duke & Cornell Moderator
Joined: 29 May 2018
Posts: 106
Location: India
GMAT 1: 700 Q48 V38
GMAT 2: 720 Q49 V39
GPA: 4
Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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15 Jul 2019, 11:11
1
1
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
Math Expert
Joined: 02 Sep 2009
Posts: 65828
Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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15 Jul 2019, 21:56
3
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.

_________________
Director
Joined: 21 Feb 2017
Posts: 677
GMAT 1: 690 Q45 V38
Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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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
Manager
Joined: 24 May 2018
Posts: 103
Location: India
Concentration: General Management, Human Resources
WE: Engineering (Energy and Utilities)
Re: A rectangular solid brick of iron is melted and shaped into a cube. If  [#permalink]

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02 Jul 2020, 06:58
1

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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