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.
Edge of the cube = 12 cm.
Volume of the cube = (edge)3 cm3
= (12 x 12 x 12) cm3
= 1728 cm3
Number of smaller cube = 8
Volume of the 1 smaller cube =1728/8 cm3 = 216 cm3
Side of the smaller cube = a
a3 = 216
⇒ a = 6 cm
Surface area of the cube = 6 (side)2
Ratio of their surface area = (6 x 12 x 12)/(6 x 6 x 6)
= 4/1 = 4:1
