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 a3
⇒ a3 = (12 × 12 × 12)/8
⇒ a3 = 63 cm3
⇒ 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