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

Solution

Side is given as `12 cm`
The Volume of the cube `=12 xx 12 xx 12=1728cm^3`
So,
The volume of smaller cube

`= 1/8 of 1728`
`= 1/8 xx 1728=216cm^3`
`=>` Let side be `S`.

`:.(S)^3 =216`
`=>S=6 cm`
Ratio of Surface Areas of cubes

`= `Surface Area of bigger cube `/` Surface Area of smaller cube

`=( 12)/6^2=2^2/1 = 4/1`
`:. `Ratio between their surface areas `4:1`.
Hence answer is obtained.