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.

Side of the solid cube = 12cm

Volume of cube = 12×12×12 = 1728 cu.cm

Solid cube is cut into 8 small cubes of equal volumes.

Volume of each small cube = 1/8 x 1728 = 216 cu.cm

Let the side of small cube is a.

Thus,

a3 = 216

a = 6cm

Surface area of cube, SA = 6 side2

Ratio of SA of the cubes = SA of solid cube/SA of small cube

= 6 (12)2/6 (6)2

= 122/62

= (2/1)2

= 4/1

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