How to calculate percentages?

Question

I want to make some pottery lotion bottles. My clay shrinks 12.5%, and I need to figure out how wide the neck should be (in the wet, unshrunk stage) in order for the plastic collar of the plunger unit to fit. I'm thinking it won't work to just figure 12.5% and add that to the collar diameter of 2.5 cm. It has to be exact. I used to know how to figure this, but I can't find my notes and for some reason I can't remember how. Help!

Thanks so much! 
Cindy

Philbert · Accepted Answer

Hello Cindy.
Thank you for this question.  The way you phrased your question threw me off the trail until I thought about it.  This is not a percentage question, this is an algebra problem.  The real question should be how do I calculate the interior diameter of the bottle if it shrinks 12.5% upon firing, or if X is the final diameter of the opening  X-0.125X = 2.5.  Then 0.875X = 2.5cm, then X = 2.5cm/0.875 or X = 2.8571428cm.
Phil

? · Answer

What do you mean by "My clay shrinks 12.5%?"  The answer changes depending on what that means.

1. Suppose that means that the VOLUME of the clay decreases by 12.5%. That means that the change in any one dimension is the cubed root of (1-0.125) = 0.875

(0.875)^(1/3) = 0.95646559138

Multiply your desired linear dimension by the reciprocal of this:

wet clay diameter = (2.5 cm)*(1/0.95646559138) ~= 2.61 cm

If by "shrinks 12.5%" you mean in any one dimension, then just get rid of the 1/3 exponent (or alternatively change that exponent to 1)

wet clay diameter = (2.5 cm)*(1/0.875) ~= 2.86 cm cm

Hope that helps!  You'll notice that Philbert above is assuming that by "shrink" you mean the change in size of the clay in any one direction, not the volume. that's why my 2nd answer matches his.

Ẩn danh · Answer

I thought Christians knew "everything". Tsk tsk. Go ask Jesus. He is still taking off the thorns from his head from the crucifixion.. lol

How to calculate percentages?

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