Volume of liquid in a sphere.

[ggauny@live.fr]

Hi,

In a exercize I have, it is asked to proove this is good (Would you see first attachement ?).

Because I don't know how to to by hand, I have asked Prime but Prime himself
don't knows the answer, taylor seem absent. (Would you see second attachement ?), but give me an answer wich is bad. Would you see third attachement ?).

I don't love ask a computer what is the solution without know do by hand
because it is too simple.

Thanks.

[JMB]

You have to use the variable 'r' instead of 'R'.

You have to use lowercase variables in CAS in order to get good results. The variable 'R' is a HOME variable with an assigned value (0 as default), so in your example CAS solved the integral substituting R with whatever numeric value it had.

[Voldemar]

   
RPN mode in Home view.

[webmasterpdx]

I don't see the problem. The first attachment seems to be correct (at least the math is).
So, what's the problem?

[ggauny@live.fr]

Hi,

I was only wondering why, writting this in the CAS command line :
(attachement 1) I don't get (attachement 2) but this (attachement 3) ?

[Voldemar]

(12-09-2017 12:32 PM)ggauny@live.fr Wrote:  I was only wondering why, writting this in the CAS command line :
(attachement 1) I don't get (attachement 2) but this (attachement 3) ?

Looks like You have the variable R value 4. Try expression with variable r (small letter).
   

[webmasterpdx]

The second attachment is intermediate information that the CAS system gives you. Sometimes, the CAS system has to make assumptions to solve the problem and it tells you information about what it had to do. Usually, you can ignore this info. However, if you think there is an error, this info can sometimes give you a clue as to what might be going on.

Now, as to your solution, you should test any variable used to see what value it has in the CAS system. e.g. If you type r <enter> it should just show r (meaning that it has not been assigned a value). This means you can use it as a variable to solve for. However, if you use R, all the capital letters are assigned values in the Home system, so either change it to R1 or r and make sure it's not been assigned a value.

[ggauny@live.fr]

Hi,

Many thanks for you all.

One very last question : Why Prime give me (after factoring two times) :

h^2*pi*(3*r-h)/3 instead of pi*h^2(r-h/3) wich is, I think, the good mathematical
writting ?

Have a good day.