Algebra Guide, 3rd Ed., P.115 #6

[omar]

To solve this problem, why can't we simply multiple the scale ratio and the volume of the real sculpture?

I converted the 0.5 cm into m by dividing by 100, yielding 0.005 m If the scale model is 0.005 m per every 1 m of the real sculpture, and the sculpture is 64 m cubed, why isn't the volume of the model simply (0.005)*(64), or 0.032 m cubed?

Thank you for your help.

[omar]

Help? Forum Experts, where are you!?

[tommywallach]

To solve this problem, why can't we simply multiple the scale ratio and the volume of the real sculpture?

I converted the 0.5 cm into m by dividing by 100, yielding 0.005 m If the scale model is 0.005 m per every 1 m of the real sculpture, and the sculpture is 64 m cubed, why isn't the volume of the model simply (0.005)*(64), or 0.032 m cubed?

Hey Omar,

So sorry we've been AWOL for awhile. Hope you don't hate us!

As to your question, you're ignoring the fact that the volume of a cube doesn't change in direct proportion to a change in its side length. That's because there are three separate dimensions that change when you change the side length. Similarly, if you half the side length of a square, the area shrinks by a factor of 4.

You can't simply multiply by 64, because that's a CUBIC measurement, not a linear measurement. Be very careful when moving between lines, areas, and volumes.

Let me know if that makes sense!

-t