Arthur D. answered • 02/19/18

Effective Mathematics Tutor

draw a cube

draw the diagonal of the bottom square

the diagonal of the bottom square forms an isosceles right triangle

the length of the hypotenuse is always x√2 where x=side length which is 3 cm

therefore the diagonal is 3√2 cm

draw the diagonal of the cube

this forms a right triangle whose legs are 3√2 which we just found and 3, a side of the cube

use the Pythagorean Theorem

d=diagonal of the cube

d

^{2}=(3√2)^{2}+3^{2}d

^{2}=18+9d

^{2}=27take the square root of each side

d=√27

d=3√3 cm (or 3*1.732=5.196 cm)