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

Answer:

Side of the new cube = 6 cm

The ratio of their surface areas is 4 : 1

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Answer 2

Volume of given cube = a3 = 123 = 12 x 12 x 12 cm3

Let the edge of the new cube = x

∴ Volume of new cube = x3

Volume of 8 new cubes = 8x3

Now, 8x3 = 12 x 12 x 12

⇒ x3 = 12 x 12 x 12/8 = 63

⇒ x = 6 cm

⇒ Surface area of given cube/Surface area of new cubes = 6a2/6x2

= 6 x 122/6 x 62 = 6 x 12 x 12/6 x 6 x 6 = 4/1 = 4 : 1

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