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# What is the length of the diagonal of a cube whose surface area is 216

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
What is the length of the diagonal of a cube whose surface area is 216  [#permalink]

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17 Jan 2019, 02:36
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Difficulty:

5% (low)

Question Stats:

93% (01:18) correct 7% (00:50) wrong based on 38 sessions

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What is the length of the diagonal of a cube whose surface area is 216?

A 6

B 9

C 12

D 6√3

E 9√3

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Joined: 18 Jul 2018
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Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Re: What is the length of the diagonal of a cube whose surface area is 216  [#permalink]

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17 Jan 2019, 02:40
2
1
Surface area of a cube = 6*side^2 = 216

Side = 6.

Diagonal of a cube = side*√3 = 6√3.

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Re: What is the length of the diagonal of a cube whose surface area is 216  [#permalink]

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17 Jan 2019, 05:45
1
Bunuel wrote:
What is the length of the diagonal of a cube whose surface area is 216?

A 6

B 9

C 12

D 6√3

E 9√3

6s^2 = 216
s= 6
diagonal of cube : s sqrt3 = 6 sqrt 3
IMO D

Bunuel
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Math Expert
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Re: What is the length of the diagonal of a cube whose surface area is 216  [#permalink]

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18 Jan 2019, 05:06
Archit3110 wrote:
Bunuel wrote:
What is the length of the diagonal of a cube whose surface area is 216?

A 6

B 9

C 12

D 6√3

E 9√3

6s^2 = 216
s= 6
diagonal of cube : s sqrt3 = 6 sqrt 3
IMO D

Bunuel

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Edited. Thank you.
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Posts: 59
Re: What is the length of the diagonal of a cube whose surface area is 216  [#permalink]

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18 Jan 2019, 12:47
Area=6a^2 =216
-> a= 6
space diagonal of cube= √3a
-> √3*6
=6√3 (D)
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Re: What is the length of the diagonal of a cube whose surface area is 216  [#permalink]

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19 Jan 2019, 16:57
I did not remember that the diagonal of a cube is side√3. Instead, I used the formula for the diagonal of a 3d rectangle
√[(length)^2+(width)^2+(height)^2]
√(6^2+6^2+6^2)
√(36+36+36)
√[36(1+1+1)
√[36(3)]
√36·√3
6√3
Re: What is the length of the diagonal of a cube whose surface area is 216   [#permalink] 19 Jan 2019, 16:57
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