Question

27 equal cubes, each with a side length r, are arranged so as to form a single larger cube with a volume of 81. If the larger cube has a side length of s, then what is r divided by s?

Answer 1

s = 3r

Answer 2

if the length of 1 cube is r then the volume of that cube is r^3. now since there is 27 such cubes, the volume of the single larger cube is 27(r^3). if the length of the larger cube is s, then the volume is s^3. we know that the volume of the larger cube is 81. therefore 27r^3=s^3=81. so r = cube root of 3. and s =3* cube root of 3. therefore s=3r

Answer 3

volume of cube is (side)^3
=> (s)^3 = 81
=> s = cuberoot(81)
=> s = 3* cuberoot(3)

since the 27 smaller equal cubes form the larger cube of volume 81
=> if volume of one small cube is V
then 27 * V = 81
=> V = 81/27
=> V = 3
since volume of cube is (side)^3
=> (r)^3 = 3
=> r = cuberoot(3)


so r cuberoot(3)
----- = ---------------
s 3 * cuberoot(3)

so r/s = 1/3

Answer 4

so r/s = 1/3