Question 2
A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cube and cut-out cubes ?
(a) 1 : 2 (b) 1 :3 (c) 1 : 4 (d) 1 : 6
Volume of the original cube having side of length 4cm=(4)3=64 cm3
[∵ volume of cube with side a=a3]
Volume of the cut-out cubes with side of length 1 cm=1 cm3
∴ Number of cut-out cubes =Volume of the original cubeVolume of a smaller cube=641=64
Now, surface area of cut-out cubes =64×6×(1)2cm2
[∴ surface area of cube with side a=6a2]
and surface area of the original cube =6×42cm2
∴ The required ratio of surface areas of the original cube and cut-out cubes
=6×4264×6=1:4