Need help with a volume question

[John45]

I tried using the mean value theorem but i got approx 9.8686cm^3
I really need help I can seem to find the answer i tried a bucnh of things

 

[RobertPaulson]

Is this not just a case of computing both volumes and calculating the difference? Because i did that and got a similar answer to the others, I think it was 37.4 but not quite. Maybe it's possible there was a typo?

 

[Deleted member 4993]

Is this not just a case of computing both volumes and calculating the difference? Because i did that and got a similar answer to the others, I think it was 37.4 but not quite. Maybe it's possible there was a typo?

Under normal condition you would be correct.

However, I think the topic wanted this to be approximated as follows:

\(\displaystyle \delta V = \ \frac{dV}{dr} \ * \ \delta r = \ 4 \ * \ \pi \ * \ r^2 \ * \ \delta r\)

\(\displaystyle \delta V = \ 4 \ * \ 3.14 \ * \ 3^2 \ * \ 0.3 \ = \ 33.912\)

Rather poor approximation of actual situation.....(error > 5%)