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Calculus/Volume of object by calculus
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Question
Hello!
I need to find the volume of a sweet potato via calculus.
I would appreciate any ideas, because I've been trying this for days, and can't think of a way to solve it.
There are two ways to do this, depending on whether this is for
(1) math or for (2) a recipe.
(1) A sweet potato is roughly a sphere spit in half with a cylinder in the middle.
For the sphere, the raidus is half the potato width, and the volume is A=4πr^3/3.
For the cylinder in the middle, take the length of the potato L minus twice the radius r, givning L-2r. Multiply this by the cross sectional area, πrē, so you get B=(L-2r)πrē.
The answer is A plus B. At least that's an approximation, anyway.
(2) To do this for real, take a container that's big enough and measure the water that is added to fill it to the top. Put in the potato (over the sink, or course) and let wome of the water overflow. Take out the potato and measure the amount left. The volume is the difference between what the container had to start with and what is left over.
This can be done for several potatoes all at once if needed.
Final) If it's (2) you're working on, I think the result of whatever you're doing will be yummy. Don't you like sweet potatoes? My mother in law use to back them with marshmallows inside and cover them with brown sugar.
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