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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

We know volume of cube =(side)3

=(12)3

=1728m3

Surface area of cube=6a2

=6×(12)2-------------(i)

The cube is cut into eight small cubes of equal volume.

Let the side of the which is cut into 8 parts be =x

The volume of a small cube =x3

The surface area of a small cube =6x2-------(ii)

Volume of each small cube=17288cm3=216cm3

Orx3=216x=6cm

Or x = 6 cm

Surface areas of the cubes ratios= SurfaceareaofthebiggercubeSurfaceareaofsmallercubes

From eq (i) and (ii),, we get

Surface areas of the cubes ratios

=6a26x2=a2x2=12262=41

Therefore, the required ratio is 4:1


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