# 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.

2
by KmvidhimaC

Log in to add a comment

by KmvidhimaC

Log in to add a comment

⇒(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

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