Help me answer this maths question. Very urgent

mkerala · **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.

Denis · **Posted:** Thu, 16 Feb 2012 18:34:16 UTC

Hint:
Pretend it's a box, lay it "flat" properly, then draw straight line connecting
the 2 points....

Denis · **Posted:** Thu, 16 Feb 2012 20:28:05 UTC

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 :idea:

Soroban · **Posted:** Fri, 17 Feb 2012 21:09:28 UTC

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: . $AG \:=\:\sqrt{9^2+9^2} \:=\:9\sqrt{2} \;\approx\;12.73\text{ cm.}$

Denis · **Posted:** Sat, 18 Feb 2012 03:16:07 UTC

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

S.O.S. Mathematics CyberBoard

Help me answer this maths question. Very urgent

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