Measurement question #2?

Question

A bug sits on one corner of a unit cube and wishes to crawl to the diagnolly opposite corner. If the bug could crawl through the cube the distance would be square root of 3. However, the bug has to stay on the surface of the cube. Find the length of the shortest path, and prove that your answer is correct.

Answer 1

Since the diagonal is given as sqrt(3) the side length must be 1. (1^2 + 1^2 + 1^2 = 3^2)
Imagine folding any two sides out so they lay flat. the endpoints would be opposite vertices of the rectangles thus formed. Since the shortest distance between any two points on a plane is a straight line connecting the points, L = sqrt(1^2 + 2^2) = sqrt(5). The proof lies above.

Answer 2

The bug would crawl diagonally across the cube then on the side of the cube to the opposite corner. That would logically seem the shortest way to me. You would have to figure out the Length of the diagonal, which would be the hypotenuse of the two triangles formed on the surface, then add the Length of the side

Answer 3

Visualize stretching a rubber band (thin, like might be used on the morning newspaper) over the outside of the cube.Common experience is that [maybe held by a thumb at the apposite apex es] the taut band will only with difficulty stay on the one vertical and one diagonal path; but will constantly try to snap to the shortest route, crossing the center of the intermediate side.

I figure x as the hypotenuse 0f a triangle with sides of 1/2 and 1 ; 1sq=1; 1/2 sq =1/4; sq root of 1.25 = 1.118 = x; so twice that equals 2.236. (not 2.414 )

Answer 4

1+root of 2

Answer 5

i know extremely. the different day i grew to become into making pancakes and the recipe called for 3 cups of milk. As all I had grew to become right into a one cup measuring cup and a 2 cup measuring cup (no 3 cup measuring cup in sight) i could no longer make the pancakes.

Answer 6

the length of one side plus the diagonal length arrived by A squared plus B squared equals C squared.