# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Mon, 20 May 2013 06:20:41 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 5 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Help me answer this maths question. Very urgentPosted: Thu, 16 Feb 2012 16:22:09 UTC

Joined: Thu, 16 Feb 2012 16:19:45 UTC
Posts: 5
An ant lives on the surface of a cube with edges of length 7cm. It is currently
located on an edge x cm from one of its ends. While traveling on the surface of the cube,
it has to reach the grain located on the opposite edge (also at a distance xcm from one
of its ends) as shown below.
(i) What is the length of the shortest route to the grain if x = 2cm? How many routes of
this length are there?
(ii) Find an x for which there are four distinct shortest length routes to the grain

Please see attach image for figure. Please tell me the steps you have followed to arrive at the solution.

Top

 Post subject: Re: Help me answer this maths question. Very urgentPosted: Thu, 16 Feb 2012 18:34:16 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3689
Location: Ottawa Ontario
Hint:
Pretend it's a box, lay it "flat" properly, then draw straight line connecting
the 2 points....

_________________
I'm not prejudiced...I hate everybody equally!

Top

 Post subject: Re: Help me answer this maths question. Very urgentPosted: Thu, 16 Feb 2012 20:28:05 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3689
Location: Ottawa Ontario
Concerning my previous post: that's the way these are USUALLY solved;
but now that I look at it after a few coffees, I "see" that the shortest
path is obviously 14: up the front, then to the grain.

Are you sure the grain is not x from the top right corner?

Or I need glasses...Shadow is sure to let me know if I do

_________________
I'm not prejudiced...I hate everybody equally!

Top

 Post subject: Re: Help me answer this maths question. Very urgentPosted: Fri, 17 Feb 2012 21:09:28 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, mkerala!

Quote:
An ant lives on the surface of a cube with edges of length 7 cm.
It is currently located on an edge x cm from one of its ends.
While traveling on the surface of the cube, it has to reach the grain located on the opposite edge
(also at a distance xcm from one of its ends) as shown below.

(i) What is the length of the shortest route to the grain if x = 2cm?
How many routes of this length are there?

(ii) Find an x for which there are four distinct shortest length routes to the grain

Unfold the front, left and top faces as shown below.
The ant is at ; the grain is at

Code:
* - - - - *
|         |
|    T    |
- Go         |
2  | o       |
-  * - o - - * - - - - *
:  |     o   |         |
7  |       o |         |
:  |    L    o    F    |
:  |         | o       |
-  * - - - - * - o - - *
: - -7- - : 2 A

The shortest distance is: .

Top

 Post subject: Re: Help me answer this maths question. Very urgentPosted: Sat, 18 Feb 2012 03:16:07 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3689
Location: Ottawa Ontario

Agree...finally (was bogged down because of solid cube, not box)!
OR:
1: ant goes NorthWest to left edge, ending 2 above: SQRT(8) = 2.83
2: then angles up left side wall to top edge, 2 from top left corne: SQRT(50) = 7.07
3: then angles directly to grain: SQRT(8) = 2.83

2.83 + 7.07 + 2.83 = ~12.73

_________________
I'm not prejudiced...I hate everybody equally!

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 5 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous