problem in volume of concentrical spherical shells

Question

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

• r=radius

• 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?

Answer 1

• The word is "radius", not "radio". I have corrected this.
• 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.

Answer 2

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.