For example, the volume of a solid of revolution with integration. Sure that's fun and all but how will that ever help in the real world? Sure, if you have math problems or a math test it can help and help derive the geometry formulas for shapes (which I also question their ability to help in the real world as no shape is ever a perfect trapezoid or rectangle--well in rare cases possibility.) I remember a problem in 9th grade geometry about finding the volume of a soda can... Well just because the height is 7 doesn't mean it's that volume.. The top concaves inward... Guessing you could make the top into half a sphere or something and find that volume and subtract but is that ever the true volume fully? In high school I always would look to see if I could find a shape that looked so true and could actually use a formula; for example, when I made a triangle with my phone and 2 books. Sure looked pretty good, did volume of a triangular prism but there was a curve on the corner and side of my phone... One that easily rendered my volume off by hardly a little more than noticeable margin but still bothersome.) anyway... I have a hard time realizing how you can put real world shapes on a xyz coordinate plane and find its volume. Even just the XY coordinate plane... How are you supposed to find the functions to fit each curve and concave, etc...) I find it hardly useful unlike maximum and minimum problems which are quite actually very useful in the math world. I mean I guess you can figure out how to make shapes with certain volumes but figuring out the volume of let's say a mold would be a bit bizarre... Finding 2 functions to exactly mimic it's curve would be impressive and then mathematically sitting at a desk for 1-6 minutes (depending on your ability with math) sounds... Unreasonable and time consuming.. Whether you can say the same about maximum and minimum is also up for debate, sure sitting down with a pencil and paper to find the minimum amount of material you have to use is time consuming. Sure, this may sound ignorant and if you got this far, I am surprised. I'm curious how this applies to the real world. Don't get me wrong, I'm a math major in computer science, not a pure mathematics major. I have been through a lot of calculus and every level of it with A+ but I can't seem to connect it to the real world as well; however I do see the usefulness sometimes. Any thoughts? Am I wrong about something? Please I'm open to anything. This isn't to sound like a ignorant fool. I am curious. A lot of calculus is useful to me, I loved to using it in physics and that was a very useful part of calculus: physics. But some things like solids of integration seem trivial but it's still cool to know.