cube

[mrg_sort]

a cube of volume of 72 .if it si divided into 8 equal cubes,the ratio of edge of smaller cube to orgininal cube is ??

[gokul_nair1984]

Vol of original cube=72
Let 'a' be an edge..=>a^3=72

The cube is divided into 8 equal cubes
ie; the volume of the new cube =72/8=9
Therefore, a^3=9

Ratio =(9/72)^(1/3)...(Smaller Edge/Original Edge)

= cube root of (1/8)=1/2

[mschwrtz]

Right. By the way, the original size of the cube is irrelevant. Each of the resulting small cubes is similar to the original cube. The volume:volume ratio of two similar solids is the cube of the line:line ration of the solids. In this case, the v:v ratio is 1/8, the cube of the e:e ratio of 1/2.