How do I derive the volume of this cup using multivariable calculus? - Mathematics Stack Exchange

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How do I derive the volume of this cup? It's been many years since I've taken calculus So far I've started with the radius of the bottom and integrated that around the circle. Did I start it rig

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calculus - How does $y^{1-q}$ become $x^{(1-q)/q}$ in this proof of the formula for the derivative of rational powers? - Mathematics Stack Exchange

15.2 #35 Multivariable Calculus. Finding the Volume of a Solid Using Double Integrals.

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Multivariable Calculus Integral volume question - Mathematics Stack Exchange

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15.2 #35 Multivariable Calculus. Finding the Volume of a Solid Using Double Integrals.