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smittytibbs
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Homework Statement
I'm trying to find the volume of a Polar shape with semi-circular cross sections. Since it is a polar graph, does that mean the cross sections are to be swept across the graph from 0 to 2π in triangular sections?
I'm aiming to create one side of a three dimensional nautilus shell by superimposing these two polar graphs: r(t) = 3 + cos (t/2) and r(t) = 1 + cos (t/2) from [0, 2π].
Could someone help me understand and explain the process involved in finding the volume please?
Homework Equations
The Attempt at a Solution
I'm pretty sure it won't work if I just integrate regularly (by integrating the area of the cross section with the radius equaling the outer polar equation minus the inner polar equation). I'm only a junior in calc BC, and i think the concept/math involved is beyond that. I'm making a model, in which the actual volume can be calculated to scale, but i just don't know about the math part.