In the cube above, the length of line segment AB is 8. The surface are

Question

https://gmatclub.com/forum/download/file.php?id=45385 In the cube above, the length of line segment AB is 8. The surface area of the cube equals what? A. 64 B. 64\sqrt{2} C. 128 D. 192 E. 192\sqrt{2} shot3.jpg

hibobotamuss · Answer

Area of a square = Diagonal^2/2
So, 64/2 = 32

Surface area = 32 x 6 = 192

D

ArjunJag1328 · Answer

Let me admit that I am quiet weak at Geometry. So feel free to correct me if my method is incorrect.

Surface area of a cube = 6 a^2 
Diagonal of a cube =  \sqrt{3} a

d =  \sqrt{3} a

\sqrt{3} a =8

a =  \frac{8}{\sqrt{3}a}

Surface area of a cube = 6 a^2

=> 6  *   (8/\sqrt{3})^2 
=>6  *   \frac{64}{3} 
=> 128

IMO C

Archit3110 · Answer

side of cube would be 2a2= 64
a= 4 \sqrt{2}

TSA of cube 6s^2
6*16*2= 192 IMO D

Archit3110 · Answer

ArjunJag1328  how did you calculate diagonal of cube as \sqrt{3}a ?
it should be \sqrt{2}a in fact as ; it would be 45:45:90 triangle .. x:x:x\sqrt{2} ..

ArjunJag1328 · Answer

I was confused whether to take diagonal of a square or cube but I chose to work it out with the diagonal of a cube because the question was to find the surface area of a cube.
My bad!!! So we are supposed to take the diagonal of a square for these types of questions. right?

Thanks indeed for taking your time to help me out.

Regards 
Arjun

Archit3110 · Answer

ArjunJag1328  : i did not understand your line  "So we are supposed to take the diagonal of a square for these types of questions. "

If you see the picture , you would see that its a triangle 45:45:90 , you can then find sides accordingly or else use relation a^2=b^2 +c^2 , since b=c so a^2=2b^2 or else side a= b \sqrt{2}
given diagnoal is 8 say 'a' 
so 8= b \sqrt{2}

so each side of cube would be , b = 8/sqrt2 or 4 \sqrt{2}..

hope this helps...

In the cube above, the length of line segment AB is 8. The surface are

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In the cube above, the length of line segment AB is 8. The surface are

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards