a crawling insect sits in a 8x8x8 room. it starts on the center of the floor of the cube.
how far must it travel to crawl to a corner on the ceiling? (answer to 3 decimal places)

5.657 units

Step-by-step explanation:

Given :  A crawling insect sits in a 8 x 8 x 8 room. It starts on the center of the floor of the cube.

Since each of the side has equal measure , so it must be a cube.

Also, each face of cube is a square having each angle as right angle.

Then, the dimension of ceiling of room will be 8 x 8 .

Let x be the diagonal of ceiling .

Then By Pythagoras theorem of right angle triangle , we have

Thus , length of diagonal of ceiling = units

Also, the diagonals of a square bisect each other, then the distance from center to corner of ceiling = half of diagonal

Then, distance from center to corner of ceiling =

Hence, it must  travel to crawl to a corner on the ceiling = 5.657