What will happen to the volume of a cube if the length of its edge is

1.	What will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume get reduced? If yes, how much?
Answer» Volume of a cube of side (s) is V₁ = a³ If the length of the side is reduced by half then s = a/2 ∴ Volume of cube (V₂ ) = s³ = (a/2)³ = a/2 x a/2 x a/2 = a³/8 = 1/8(a³) ∴ V₂ = 1/8 × V₁ ∴ V₁ = 8V₂

What will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume get reduced? If yes, how much?

Answer»

Volume of a cube of side (s) is V₁ = a³

If the length of the side is reduced by half then s = a/2

∴ Volume of cube (V₂ ) = s³

= (a/2)³

= a/2 x a/2 x a/2

= a³/8 = 1/8(a³)

∴ V₂ = 1/8 × V₁

∴ V₁ = 8V₂