Scaling Problems

[007math]

Just had a question: how do you guys suggest memorizing the study guide problem/solutions? I don't want to memorize like 50 formulas, so any tips?

And another question: Are there any keywords in the #46 scaling problems to signify whether the units are in volume, area, or ugh...the single dimension (scalar? idk). I can get these only 30-50% of the time since I always don't do the right power (as in i cube rather than square or square rather than cube, etc.). Thanks!

EDIT: Thread renamed to make it more apt.

[Shawn]

For memorizing study list: I don't know, just do it.
On scaling: Words are what determines the relationship, so think of it as undoing the thing you have both of and then converting to what you have to solve. Mainly just pay attention to units and phrases such as "thickness remains constant" or "cost varies with the square of the cross section." I think the best way I can help you here is put up your most confusing problems and I can offer you a detailed explanation. I hope this helps some. In the end just think what dimension am I in and then what dimension do I need to be in? Really doing problems should help, but if you just can't imagine the situation, having someone explain it can really help on these kinds of problems.
Brief Scaling: I am going to state the obvious (don't mean to offend), but if I do that is why you need to put problems.
Linear: Length (Inches, centimeters, meters, mile, etc.)
Square: Area (Acres, Square Feet, Square Inches, Surface Area, Plating something, etc.)
Cubic: Volume (weights, cubic meters, cubic feet, gallons, milliliters, etc.)

[007math]

Okay, so for example this question:

12G-46: A metal stamping company makes different sized Texas lone stars for yard art from a single spool of metal sheet. If the 2ft star weighs 4.4lbs, how tall is the star that weighs 25lbs? Ans: 4.77

I would assume since it says feet and weight that one would do [unparseable or potentially dangerous latex formula] but that gives me the incorrect answer; however, I do get the answer when squaring it instead. Why does it happen this way? (sorry if I'm asking dumb questions...this is a easy 5 points I always miss).

[nsguy1350]

[Shawn]

If you cut out a star from a sheet, then only the length and width are going to change, not thickness. So since the question would be in 3D (weight) you take off a dimension (2D), which is square not cubed. Anything like "constant thickness, plating, made from sheet, comes from spool, etc. implies constant thickness, therefore you take a dimension off.
For this problem specifically, it comes off a sheet, so the sheets are only going to be longer and wider, not thicker. So let's say you are punching out rectangular prisms. The cross section is a square and the thickness is constant. If we punch out 2 in squares vs 4 in squares what is the percent increase in weight? Square relationship 16/4. Also note when the problem says something such as cost of a brick varies only with length. You would think cost of a brick would be volume or mass, but in this case it would be linear feet. These are not ambiguities, they are just an additional considerations. Feel free to post as many scaling problems as you need to, to understand them. An easy 5 points can help out a lot.
Ed.lit: Added additional information

[007math]

10H-46. A 55-gallon drum is 23 inches in diameter and is 35 inches tall. If a glass manufacturer wanted to make a small 12-oz drinking glass that looked like a 55-gallon drum, how tall should the glass be? Ans. 4.18 inches

EDIT: Renamed thread to scaling problems so this can be used to ask 46's.

[nsguy1350]

[Shawn]

Volume, it doesn't say that the diameters or anything are the same. Volume is cubic, so cube the heights. It could have asked you what the new diameter would be. Also the unit conversion part is particularly important, since a lot of these questions have different units.