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## Main Question or Discussion Point

Hi all,

Is it possible to determine the volume of a shape where, in the x and y dimensions, the shape is described by an equation, and then its elevation is described by another equation?

An example would be a parabola in the x-y plane whose elevation is based on another parabolic function. For example lets say [tex]y=x^2+4[/tex] from [itex]x=-2[/itex] to [itex]x=2[/itex] with an elevation determined by a circle of radius 4 (so zero elevation at the apex and the x-axis). Meaning [tex]z=\sqrt{16-y^2}[/tex] (independent of x).

Can I get this volume by integration, or would I just need to apply some kind of finite element approach? Thanks in advance; most all of the volume integrals I could find online or in a text are just volumes of revolution.

Is it possible to determine the volume of a shape where, in the x and y dimensions, the shape is described by an equation, and then its elevation is described by another equation?

An example would be a parabola in the x-y plane whose elevation is based on another parabolic function. For example lets say [tex]y=x^2+4[/tex] from [itex]x=-2[/itex] to [itex]x=2[/itex] with an elevation determined by a circle of radius 4 (so zero elevation at the apex and the x-axis). Meaning [tex]z=\sqrt{16-y^2}[/tex] (independent of x).

Can I get this volume by integration, or would I just need to apply some kind of finite element approach? Thanks in advance; most all of the volume integrals I could find online or in a text are just volumes of revolution.