For example, finding the volume of a sphere with a cylinder inside. I get stuck
on these types of problems, not because I can't visualize the solid on the axis,
but when it comes to the numbers. I know that a x-section is a slice that
gets repeated throughout the volume of the 3-d solid after being integrated
to find the actual volume, but I tend to mess up on the right formula
usage (ie use area or volume) and what to integrate with respect to (sometimes
I can't tell what the difference is between the value h and r since heights can equal
radii at times).
ummm... ok....
First you figure the volume of the cylinder.
(That's pi*radius^2*height.)
Then you figure out the volume of the sphere.
(That's 4/3*pi*radius^3.)
Then you subtract the first from the second.
So if yer trying to figure it out for geometry, just measure your pieces and start figuring. If it's for algebra, just copy & paste this code:
First you figure the volume of the cylinder.
(That's pi*radius^2*height.)
Then you figure out the volume of the sphere.
(That's 4/3*pi*radius^3.)
Then you subtract the first from the second.
So if yer trying to figure it out for geometry, just measure your pieces and start figuring. If it's for algebra, just copy & paste this code:
CODE
4/3πr³ -(πr²h)
Easy as pi!
I appreciate the help 
but I'm trying to figure out how to use calculus to answer questions like these. Oh and the cylinder in a sphere example I gave is nothing more than an example, it's my fault that I did not make that clear, I apologize. The main
question I asked is what to look for when using calculus on these types of problems.
but I'm trying to figure out how to use calculus to answer questions like these. Oh and the cylinder in a sphere example I gave is nothing more than an example, it's my fault that I did not make that clear, I apologize. The main question I asked is what to look for when using calculus on these types of problems.
What you have to look for a function that describes a 3-dimensional piece of a differentially small volume, otherwise you won't be able to integrate to find the volume. In these types of problems, some function will have to be given, or if the solid is perfectly symmetric about some axis you can find the equation that describes that solid and revolve it around the axis of symmetry. Sorry if it sounds a lot like babble.
The way I see it, if the guy asking the question is trying to accomplish it using calculus, and has even the remotest idea of what pi is, he'll se right through that gibberish that doesn't actually mean squat.
(seriously.... How you gonna figure out the volume of something using 3rd grade algebra, but not using pi?
)
(seriously.... How you gonna figure out the volume of something using 3rd grade algebra, but not using pi?
)