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Question

A solid cube of side 12cm 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.


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Solution

Step I: Finding side of the new cube

Side of the big solid cube =12cm

We know volume of a cube =Side×Side×Side

So, Volume of the solid cube =12×12×12=1728cm3

Given that the solid cube is cut into 8 small cubes of equal volumes.

Thus, Volume of each small cube =18×1728=216cm3

Let the side of small cube is a.

So the volume of a small cube =a×a×a=a3

Thus, equating the volumes of the small cube, we get:

a3=216

a=6cm

Thus, side of the new cube is 6cm.

Step II: Finding the ratio of surface areas.

We know, the Surface area of cube is given by SA=6×side2

Surface area of the big solid cube of side 12cm=6×122=864cm2

Surface area of the small cube of side 6cm=6×62=216cm2

Ratio of SAof the cubes = SAofsolidcubeSAofsmallcube

=864216=41=4:1

Thus, the ratio of surface areas of two cubes is 4:1.


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