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the prism has a volume of 120 cm3.
what would the volume of the prism be if each dimension were halved?

The volume of the prism is  (Length x Width x Height).
To make it easier to work with, let me write (L x W x H).

If you cut each dimension in half, then the volume is

       (1/2 x L) x (1/2 x W) x(1/2 x H) .

It's pretty easy to rearrange that, and see what's going on:

               1/2 x L x 1/2 x W x1/2 x H =

         (1/2 x 1/2 x 1/2) x (L x W x H)  = 

                ( 1/8 )        x (original volume) =

                 ( 1 / 2³ )  x  (original volume)

Here's the general rule:

If you multiply all the linear dimensions of a drawing OR an object
by some factor 'K' , then

-- all of the linear features, like perimeter, diagonal, circumference,
diameter etc. are all multiplied by  'K' .

-- the 2-dimensional things on it, like area of the drawing, or surfaces
of a prism, sphere or any blob, are all multiplied by  K² .

-- the 3-dimensional features, like volume of any prism, pyramid,
sphere, blob, ellipsoid, cylinder etc. are all multiplied by  K³ .

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