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15 Jul 2019, 10:19
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C
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Difficulty:
35%
(medium)
Question Stats:
77% (02:24) correct
23%
(02:37)
wrong
based on 269
sessions
History
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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
A. 36
B. 156
C. 216
D. 432
E. 2592
15 Jul 2019, 22:56
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mangamma
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.
General Discussion
vinayakvaish
Joined: 29 May 2018
Last visit: 19 Oct 2020
Posts: 91
Given Kudos: 52
Location: India
Schools: Marshall '22 (A$) IIMA PGPX "21 (D) Duke '22 (D) IIMB EPGP "21 (A) McCombs '22 (A) IIMC MBAEx "21 (WD) Georgia Tech '22 (A$) Johnson '22 (WD)
GMAT 1: 700 Q48 V38
GMAT 2: 720 Q49 V39
GPA: 4
Schools: Marshall '22 (A$) IIMA PGPX "21 (D) Duke '22 (D) IIMB EPGP "21 (A) McCombs '22 (A) IIMC MBAEx "21 (WD) Georgia Tech '22 (A$) Johnson '22 (WD)
GMAT 2: 720 Q49 V39
Posts: 91
15 Jul 2019, 12:11
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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
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
