A solid cube of side `12 c m` is cut into 8 cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.

Explanation

Volume of the big cube `= (12 xx 12 xx 12) cm^(3) = 1728 cm^(3)`
Volume of a small (new) cube `= (1728)/(8) cm^(3) = 216 cm^(3)`
Let each side of the new cube b a cm
Then, its volume `= a^(3) cm^(3)`
`:. a^(3) = 216 = (6)^(3) rArr a = 6`
Thus, the side of the new cube is 6 cm.
Surface area of the big cube
`= {16 xx (12)^(2)} cm^(2) = (6 xx 144) cm^(2) = 864 cm^(2)`
Surface area of the smaller cube
`= {6 xx (6)^(2)} cm^(2) = (6 xx 36) cm^(2) = 216 cm^(2)`
Ratio between the surface areas of big cube and small cube
`= 864 : 216 = (864)/(216) = (4)/(1) = 4 : 1`