The volume of a cube is side length cubed (s^3)
So if you know the volume then take the cube root of 1/512... which is 1/8
So each side of the cube is 1/8.
There are 6 congruent sides on a cube (picture a “dice”). Do the area of each side would be (1/8)(1/8)= 1/64 then multiply that area by 6 and reduce ... you get 6/64 = 3/32 for the surface area
