Question

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.

{can u please tell me the procedure which u follow to solve this problem.please}

Answer 1

An ant lives on the surface of a cube with edges of length $7\mathrm{cm}$. It is currently located on an edge $\mathbf{x}$ 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 $\mathrm{x} = 2\mathrm{cm}$? How many routes of this length are there?

The shortest way is

$$S = (7 - x) + 7 + 7 + x = 21 \mathrm{cm}.$$

The are two such ways.

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

For $x = 3.5$ cm there are 4 such ways.