Oh, and this whole thing about 5% decrease is an erroneous calculation in the first place, though, as others have pointed out.
[QUOTE=treis]
.9*r[sub]old[/sub][sup]2[/sup]=r[sub]new[/sub][sup]2[/sup]
square root both sides:
.95*r[sub]old[/sub]=r[sub]new[/sub]
[/QUOTE]
This is wrong. You forgot to square root the .95.
[QUOTE=dauerbach]
Damn, it seems that my brain is fried tonight.
[/QUOTE]
I don’t know if this is “Damn, I see it now” or “Damn, I give up”. If it’s the latter, well, I wouldn’t give up so quickly. Here, let’s just get rid of the percentages for a second, and look at the example again. (This example doesn’t accurately reflect the problem in the OP, but it’s just to clear up the last point of confusion)
Suppose the radius starts out 100 inches and changes to 95 inches. The diameter, therefore, starts out 200 inches (twice the radius) and changes to 190 inches (twice the radius, again, of course. The diameter is definitionally incapable of being anything except twice the radius.)
So far, so good, right?
[QUOTE=Indistinguishable]
Oh, and this whole thing about 5% decrease is an erroneous calculation in the first place, though, as others have pointed out.
This is wrong. You forgot to square root the .95.
[/QUOTE]
Look more closely. The 0.95 in the second line is the square root of the 0.9 in the first line…to two decimal places, anyway.
[QUOTE=aerodave]
Look more closely. The 0.95 in the second line is the square root of the 0.9 in the first line…to two decimal places, anyway.
[/QUOTE]
Oh, heh. Looks like my brain’s a little fried too. 
[QUOTE=Indistinguishable]
Oh, and this whole thing about 5% decrease is an erroneous calculation in the first place, though, as others have pointed out.
This is wrong. You forgot to square root the .95.
[/QUOTE]
Wow, I need to refresh more often.
[QUOTE=Snarky_Kong]
Wow, I need to refresh more often.
[/QUOTE]
I was just about to reply to your original post, but refreshed just in the nick of time.
[QUOTE=Indistinguishable]
Oh, and this whole thing about 5% decrease is an erroneous calculation in the first place, though, as others have pointed out.
[/QUOTE]
Heh. I suppose I saw someone’s long figure which wasn’t a simple .95, and assumed the original problem had mentioned a 5% decrease in volume, other posters had given the square root of 0.95 correctly, and treis had just forgotten to take the square root. Heaploads of confusion ensued.
Wow you’re doing it the hard way.
Formula for a prism is area of base x height
The height remains the same so the area of the base must be 90% of the original base. The ratio of the areas of two circles is proportional to the ratio of the square of their respective radii.
So r2/r1 = sqrt(0.9) or sqrt(0.9) x r1
r2 - r1 = r1 - sqrt(0.9) x r1 = [1-sqrt(0.9)] x r1
Yielding approximately 5.13167% reduction
[QUOTE=SaintCad]
Wow you’re doing it the hard way.
Formula for a prism is area of base x height
The height remains the same so the area of the base must be 90% of the original base. The ratio of the areas of two circles is proportional to the ratio of the square of their respective radii.
So r2/r1 = sqrt(0.9) or sqrt(0.9) x r1
r2 - r1 = r1 - sqrt(0.9) x r1 = [1-sqrt(0.9)] x r1
Yielding approximately 5.13167% reduction
[/QUOTE]
This has been mentioned like 85 times in the thread. What was everybody else doing harder?
[QUOTE=dauerbach]
Alright, I am brain dead. If the radius decreases by 5% then the diameter decreases by 2.5%.
[/QUOTE]
Sorry, you are brain dead. 
If the radius decreases by 5% then the diameter decreases by 5%. d=2r. 0.9d = 0.9(2r). You must multiply both sides of the equation by the same factor to keep it balanced.