Diagonal of a cube

Expert replies

AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Wed Jun 11, 2008 9:27 am

The diagonal of a cube of side x is xsqroot3.

This can be found by applying the Pythagorean Theorem twice (first to find the diagonal of a face of the cube, xsqroot2, and then to find the diagonal through the center, xsqroot3).

Can someone please demonstrate for me the latter part (xsqroot3).

Assume we are dealing with a cube with side 4.

Thanks.

https://second-lap.blocked/

Like this post

Source: Beat The GMAT — Problem Solving | Wed Jun 11, 2008 9:27 am

AleksandrM: Legendary Member; Posts: 566; Joined: Fri Jan 04, 2008 11:01 am; Location: Philadelphia; Thanked: 31 times; GMAT Score:640

by AleksandrM » Wed Jun 11, 2008 9:31 am

Never mind I got it. Just imagine a cube that has been cut through the side

You have base 4 and hight 4sqroot2:

(4sqroot2)^2 + 4^2 = x^2 diagonal from one end of cube to ther other

x = 4sqroot3

https://second-lap.blocked/

Like this post

egybs: Master | Next Rank: 500 Posts; Posts: 178; Joined: Wed May 14, 2008 3:51 pmFollowed by: 1 member; Thanked: 16 times; GMAT Score:99%+

by egybs » Wed Jun 11, 2008 9:46 am

Diag1 = Diagonal of one side of the cube
Diag2 = Diagonal of the entire cube

Diag1^2 = x^2+x^2
Diag1 = (2x^2)^.5 = x(2^.5)
Diag2^2 = (x(2^.5))^2 + x^2
Diag2^2 = 2x^2 + x^2 = 3x^2
Diag2 = (3x^2)^.5 = x(3^.5)

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Wed Jun 11, 2008 12:09 pm

You could also use the three-dimensional version of the Pythagorean Theorem:

d^2 = x^2 + y^2 + z^2

where d is the diagonal inside a box ('rectangular prism', in math terms) of dimensions x by y by z.

Thus in the special case of a cube measuring x by x by x,

d^2 = x^2 + x^2 + x^2
d^2 = 3x^2
d = root(3)*x

This won't be useful very often on the GMAT, but occasionally it does help.

Like this post

egybs: Master | Next Rank: 500 Posts; Posts: 178; Joined: Wed May 14, 2008 3:51 pmFollowed by: 1 member; Thanked: 16 times; GMAT Score:99%+

by egybs » Wed Jun 11, 2008 12:24 pm

Heh good point Ian... that's a lot nicer!

Ian Stewart wrote:You could also use the three-dimensional version of the Pythagorean Theorem:

d^2 = x^2 + y^2 + z^2

where d is the diagonal inside a box ('rectangular prism', in math terms) of dimensions x by y by z.

Thus in the special case of a cube measuring x by x by x,

d^2 = x^2 + x^2 + x^2
d^2 = 3x^2
d = root(3)*x

This won't be useful very often on the GMAT, but occasionally it does help.

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review