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the cube in inches?

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by sanju09 » Mon Oct 24, 2011 3:54 am
Volume of a cube is x cubic yards and its surface area is y square feet. If x = y, what is the length of each edge of the cube in inches?
(A) 54
(B) 216
(C) 432
(D) 864
(E) 1944
Last edited by sanju09 on Mon Oct 24, 2011 4:44 am, edited 1 time in total.
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by neelgandham » Mon Oct 24, 2011 4:24 am
1 yard = 3 feet
1 cubic yard = 27 cubic feet

Say, the side of the cube = a,
Volume = a*a*a = x Cubic Yards = x*27 Cubic feet -(1)
Surface area = 6*a*a = y Cubic feet = x Cubic feet(x=y) -(2)

from 1 and 2

(a*a*a)/(6*a*a) = x*27/x => a/6 = 27 => a = 27*6 = 162 feet = [spoiler]162*12 inches = 1944[/spoiler]

:banghead: where did I go wrong ??

Edited: Relaxed now :D
Last edited by neelgandham on Mon Oct 24, 2011 4:50 am, edited 1 time in total.
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by sanju09 » Mon Oct 24, 2011 4:46 am
neelgandham wrote:1 yard = 3 feet
1 cubic yard = 27 cubic feet

Say, the side of the cube = a,
Volume = a*a*a = x Cubic Yards = x*27 Cubic feet -(1)
Surface area = 6*a*a = y Cubic feet = x Cubic feet(x=y) -(2)

from 1 and 2

(a*a*a)/(6*a*a) = x*27/x => a/6 = 27 => a = 27*6 = 162 feet = 162*12 inches = 1944

:banghead: where did I go wrong ??
Don't bang head, you are correct, choices edited, thanks
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by mankey » Mon Oct 24, 2011 6:27 am
On solving it gives: B.

What is the OA?
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by GMATGuruNY » Mon Oct 24, 2011 6:58 am
sanju09 wrote:Volume of a cube is x cubic yards and its surface area is y square feet. If x = y, what is the length of each edge of the cube in inches?
(A) 54
(B) 216
(C) 432
(D) 864
(E) 1944
Let e = the length of each edge in YARDS.
Volume in CUBIC YARDS = e³.

Since 1 yard = 3 feet, the length of each edge in FEET = 3e.
Surface area in SQUARE FEET = 6(3e)² = 54e².

Since the volume in CUBIC YARDS = the surface area in SQUARE FEET:
e³ = 54e²
e = 54 yards.

Since 1 yard = 36 inches, the length of each edge in INCHES = 54*36 = 1944.

The correct answer is E.
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