Question

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

Answer 1

Volume of old cube =a³
⇒(12)³=1728 cm³
No.of cubes =8
Volume of old cube = 8* volume of 1 new cube
1728=8*a³
1728/8=a³
12/2=a
6 cm=a
Surface area of old cube/ surface area of new cube=6*(12)²/6*(6)²
=144/36=4/1=4:1

Answer 2

Side of a large cube(a) = 12cm
volume of the cube = (12³)cm³
 => 1728 cm³
eight small cubes of equal volumes are cut from the larger one 
∴volume of larger cube = 8* volume of one small cube.
=>1728 = 8 * volume of small cube
=>1728/8 = volume of small cube
∴volume of one small cube = 216.
then side of the smaller cube = ∛216 = 6cm
 The ratio of surface area of larger cube  and small cube = 864:216 = 4:1