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.

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Solution

Edge of cube=12cm

Volume of cube=axaxa

=12X12X12

=1728cm cube

Then it is cut into 8 equal sides therefore smaller cube =1728/8

=216cm cube

volume of cube =axaxa

therefore,216=axaxa

a=216*cube root

= 6cm

surface area of smaller cube =6(a)sq

= 6X(6)sq

=6X36=216cm sq

surface area of bigger cube =6X(12)sq

6X144=864cm sq

Ratio b/w their surface areas=216:864

=216/864

=1/4

=1:4

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