Question

what will happen to the volume of a cube if the lenght of its edges is reduced to half?Is the volume get reduced? if yes, how much ?

Answer 1

Let the edge of the cube be 'x' units.

Volume of a cube = (edge)³

Volume of the cube with egde x = x³

Now let the new edge be ' y ' units.

But y = 1/2 x
since the edge of the cube is reduced by half.

Now,
Volume of the new cube = y³
= ( 1/2 x ) ³
= x³ / 8
= x³ * 1/8

But x³ is the volume of the first cube whose edge was x units.

∴ Volume of the new cube = 1/8 * Volume of the first cube

Thus yes the volume of the new cube gets reduced and it become 1/8 th the volume of the first cube.