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 area.

Answer 1

Volume of solid cube of side

12 cm = 12 cm x 12 cm x 12 cm

Number of cubes of equal volume = 8

Volume of one such cube 

= \(\frac { 12\times12\times12 }{ 8 }\) cm³ = 216 cm³

Edge of the new cube = 3√216 cm³ = 6 cm

Surface area of one big cube of side/edge 12 cm 

= 6 x (12 cm)² = (6 x 144) cm²

Also surface area of one smaller cube 

= 6 x (6 cm)² = (6 x 36) cm²

Required ratio = \(\frac { 6 \times144 }{ 6 \times 36 }\) = 4 : 1.