1. ## What's wrong in my answer to this question? (About find volumes of solids)

Ok, guys.

I am on my first year on Engineering Mechanics and by now I got stuck at this problem:

A hole of radius r is bored through the center of a sphere of
radius R > r . Find the volume of the remaining portion of the
sphere.

The reason is that my answer doesn't match with the book's one.

OK, here is what I did:

A picture worths more than 1000 words

I know another way to solve it, and it gives me the right answer. But I can't find any gap at the answer I did above

Thank you for you atention, and Math bless you all.

2. Originally Posted by AmaymonF
Ok, guys.

I am on my first year on Engineering Mechanics and by now I got stuck at this problem:

A hole of radius r is bored through the center of a sphere of
radius R > r . Find the volume of the remaining portion of the
sphere.

The reason is that my answer doesn't match with the book's one.

OK, here is what I did:

A picture worths more than 1000 words

I know another way to solve it, and it gives me the right answer. But I can't find any gap at the answer I did above

Thank you for you atention, and Math bless you all.

I can't understand what you wrote above: it is too dim and scarcely explained, but check the following which

is the usual mistake of many in this particular problem: the bored hole through the sphere is not a straight

cylinder but one with both top and basis "rounded".

I think I guess this is what you missed when you wrote the formula for $\displaystyle A(x)$ ...

Tonio

3. EUREKA!!!

Oh yeah, man. You enlighted me. I cannot integrate from 0 to R but from 0 to sqrt(R^2 - r^2).
Thank youuu =D