• Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer

Diagonal of a cube

This topic has 1 expert reply and 3 member replies
AleksandrM Legendary Member
Joined
04 Jan 2008
Posted:
566 messages
Upvotes:
31
Test Date:
September 8, 2008
Target GMAT Score:
650
GMAT Score:
640

Diagonal of a cube

Post 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.

  • +1 Upvote Post
  • Quote
  • Flag
AleksandrM Legendary Member
Joined
04 Jan 2008
Posted:
566 messages
Upvotes:
31
Test Date:
September 8, 2008
Target GMAT Score:
650
GMAT Score:
640
Post 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

  • +1 Upvote Post
  • Quote
  • Flag
egybs Master | Next Rank: 500 Posts Default Avatar
Joined
14 May 2008
Posted:
178 messages
Upvotes:
16
Test Date:
08/2008
GMAT Score:
99%+
Post 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)

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Ian Stewart GMAT Instructor
Joined
02 Jun 2008
Posted:
2285 messages
Followed by:
347 members
Upvotes:
1090
GMAT Score:
780
Post 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.

  • +1 Upvote Post
  • Quote
  • Flag
egybs Master | Next Rank: 500 Posts Default Avatar
Joined
14 May 2008
Posted:
178 messages
Upvotes:
16
Test Date:
08/2008
GMAT Score:
99%+
Post 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.

  • +1 Upvote Post
  • Quote
  • Flag

Top First Responders*

1 GMATGuruNY 71 first replies
2 Rich.C@EMPOWERgma... 48 first replies
3 Brent@GMATPrepNow 37 first replies
4 Jay@ManhattanReview 26 first replies
5 ErikaPrepScholar 10 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description GMATGuruNY

The Princeton Review Teacher

129 posts
2 image description Rich.C@EMPOWERgma...

EMPOWERgmat

116 posts
3 image description Jeff@TargetTestPrep

Target Test Prep

106 posts
4 image description Max@Math Revolution

Math Revolution

92 posts
5 image description Scott@TargetTestPrep

Target Test Prep

92 posts
See More Top Beat The GMAT Experts