**A solid cube of side 12 cm is cut into 8 identical cubes. What will be the side of the new … the total surface area of all the small…**

###### Answers:

Here, cube of side 12 cm is divided into 8 cubes of side 9 cm.

Given that,

Their volumes are equal.

Volume of big cube of 12 cm = Volume of 8 cubes of side a cm

(Side of big cube)^{3} = 8 x (Side of small cube)^{3}

(12)^{3} = 8 x a^{3}

⇒ a^{3} = (12 × 12 × 12)/8

⇒ a^{3} = 6^{3} cm^{3}

⇒ a = 6 cm

∴ Side of small cube = 6 cm

Ratio of their surface

= Surface area of the original cube/Total surface area of the small cube

= 6(Side of big cube)2/8 × 6 (Side of small cube)2

= (6 × 12 × 12)/(8 × 6 × 6 × 6) = 4/8 = 1 : 2

So, the ratio is 1 : 2