Question

A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the surface areas of the original cubes and cut-out cubes?

Options

• 1 : 2

• 1 : 3

• 1 : 4

• 1 : 6

Answer 1

1 : 4

Explanation:

Volume of the original cube having side of length 4 cm = (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 cube"/"Volume of a smaller cube" = 64/1` = 64

Now, surface area of cut-out cubes = 64 × 6 × (1)² cm²  ...[∵ Surface area of cube with side a = 6a²]

And surface area of the original cube = 6 × 4² cm²

∴  The required ratio of surface areas of the original cube and cut-out cubes

= `(6 xx 4^2)/(64 xx 6)`

= 1 : 4