Question

If all the dimensions of the rectangular pyramid are multiplied by 1/5, what is the effect on the volume

Answer 1

1/125 to be exact

Explanation:

Answer 2

If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 125 times smaller.

Explanation:

A rectangular pyramid has the following dimensions:

length(l), height(h) and width(w)

The volume is:

`V = (l*h*w)/(3)`

If all the dimensions of the rectangular pyramid are multiplied by 1/5

Then we have that:

`l = (l)/(5), w = (w)/(5), h = (h)/(5)`

The modified volume will be:

`V_(M) = ((l)/(5)*(w)/(5)*(h)/(5))/(3) = ((l*w*h)/(125))/(3) = (l*h*w)/(125*3) = (1)/(125)((l*h*w)/(3)) = (V)/(125)`

So

If all the dimensions of the rectangular pyramid are multiplied by 1/5, the volume will be 1/125 of the original, that is, 125 times smaller.