If a cube has a volume of 27 cubic centimeters, what is the length of each edge? use the volume formula, v = s3

Hello!

Given the volume of cube being 27 cubic centimeters (27 cm³), to find the length of each side, substitute the value of the volume back into the formula, and take the cube root of both sides.

27 cm³ = s³ (take the cube root of both sides)

s = 3 cm

Therefore, the length of each edge of the cube is 3 centimeters.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4