Answer: 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
[tex]x^2=8^2+8^2\\\\\Rightarrow\ x^2=128\\\\\Rightarrow\ x=\sqrt{128}=8\sqrt{2}[/tex]
Thus , length of diagonal of ceiling = [tex]8\sqrt{2}[/tex] 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 = [tex]\dfrac{8\sqrt{2}}{2}=4\sqrt{2}[/tex]
[tex]=4\times1.4142135623=5.6568542492\approx5.657[/tex]
Hence, it must travel to crawl to a corner on the ceiling = 5.657
