# problem in volume of concentrical spherical shells

I was trying to find the volume of concentrical sphere shells but to my surprise i come up with equal volume when evidently the outer shell should have more volume than the inner shell. I can't figure out what I'm doing wrong. This is what I did: Concentrical spheres representation

• r1=10

• r2=11

• r3=12

• v=volume

• $v=\frac{4}{3}\pi r^3$

• v1=41887

• v2=46076

• v3=50265

• vb=volume of the outer shell

• vb=v3-v2=4189

• va=volume of the inner shell

• va=v2-v1=4189

As you can see the volume of the two shells comes out as equal but evidently the outer shell is larger than the inner shell so it should have more volume. I don't know what I'm doing wrong. Can someone tell me 1.if the shells should have different volume, 2.what am I doing wrong, 3.what are the actual volumes of the shells and 4.how to come to said volume?

• Not a single one of your volumes is correct. I cannot figure out the mistake you made to get them wrong. The first one is off by a factor of 10, but the other two bear no similar relation to their correct values:

$$v_1 = 4188.79...$$ $$v_2 = 5575.28...$$ $$v_3 = 7238.23...$$ You get them by plugging in the appropriate values of $r$ into the volume formula you gave.

Looks like what was wrong was GOOGLE CALCULATOR. I tried several times to check the results using the google calculator and it was giving me wrong results (for anyone that want to check the bug here is what i did: v1= 4 ÷ 3 x π x 10 exp 3 = ; v2= 4 ÷ 3 x π x 11 exp 3= ).

So, with the new numbers I came with I can get the volume results:
vb = v3 − v2 = 1663 (outer shell volume)
va = v2 - v1 = 1387 (inner shell volume)
Now these results make sense, as the outer shell should have more volume than the inner shell.

• While there is no reason not to post an answer to your own question, the standards are as high for you as they are for any other Reader. Less chattiness and more detail about what specifically was wrong with the work done for your Question would improve this post. If you plan on sticking around to participate in Math.SE, have a look at how to use MathJax and $\LaTeX$ for posting mathematical notation. Oct 7 '15 at 5:19
• The problem was not google calculator, but a mistake in your use of it. the "EXP" key is used for entering scientific notation. Instead of $10^3, 11^3, 12^3$, you were telling it to give you $10 \times 10^3, 11 \times 10^3, 12 \times 10^3$. The key you were after is "$x^y$". Oct 7 '15 at 20:56
• @hardmath - While I certainly agree with you that learning to juse MathJax would be a major improvement, and that this would have been better as a comment, what he gave in it is exactly specifics about what was wrong with the work done. And his providing it allowed me to recognize his error and therefore to offer him appropriate correction. Oct 7 '15 at 21:01
• @PaulSinclair: Note that the OP edited their self-answer to remove some of the chattiness I complained about. I'm glad you were able to discern the mistaken use of EXP in calculating. Still, whatever advantage was afforded by the self-answer would have been equally well expressed in editing the Question. Oct 7 '15 at 21:07