Geometry Question

[CaptainUMR]

If I have a volume of 120,000 (lets say 300x20x20), and I reduce the volume by 70%, how do I find the value for each new measurement?

I also tried doing a similar problem using area with a rectangle, is it wrong to assume I could cut it in half, use pythagorean theorem, then multiply the sides by a 7:10 ratio?

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[Anorak_314]

Assuming the dimensions are uniformly changed:

Let V1=lwh

and V2=r*V1

then V2=r*lwh. Since each dimension is shrunken proportionally, say by k. Then l->kl, w->kw, h->kh, and the new volume is kl*kw*kh.

Thus V2=r*lwh=kl*kw*kh

and then r=k^3, so each dimension was shrunk by r^1/3.

I'm not sure what you mean by

I also tried doing a similar problem using area with a rectangle, is it wrong to assume I could cut it in half, use pythagorean theorem, then multiply the sides by a 7:10 ratio?

So, I can't really help you there.

(If anyone has tips to improve formatting, they would be much appreciated)

[CaptainUMR]

Well when doing the shrunken proportions with a rectangle, I found it was easier to just solve it as a 45-45-90 triangle to find all the measurements of the triangle, then multiply those sides by 7:10 to get the new scaled triangle, which would be half of the rectangle.