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

User Shazad
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2 Answers

5 votes

Answer:

1/125 to be exact

Explanation:

User Peter Ledbrook
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3 votes

Answer:

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.

User TUrwin
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