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## Main Question or Discussion Point

Hello,

I've just found a book which mentions the formula for calculating the volume of a rotated polar function:

[tex]\int_{\theta_1}^{\theta_2} \frac{2}{3} \pi r^3 sin(\theta) d\theta [/tex]

How does one calculate this? In an https://www.physicsforums.com/showthread.php?t=457896", I calculated that the volume would be

[tex]\int_{\theta_1}^{\theta_2} \pi r^2 sin(\theta) d\theta [/tex]

if one just added up cones with the side of the cone being the function [tex]f(\theta)[/tex]. This method would be similar to shells, but apparently I'm [tex]\frac{2}{3} r [/tex] off.

If anyone could help me understand how to calculate volume I would be eternally grateful.

Thanks for taking the time to read this!

I've just found a book which mentions the formula for calculating the volume of a rotated polar function:

[tex]\int_{\theta_1}^{\theta_2} \frac{2}{3} \pi r^3 sin(\theta) d\theta [/tex]

How does one calculate this? In an https://www.physicsforums.com/showthread.php?t=457896", I calculated that the volume would be

[tex]\int_{\theta_1}^{\theta_2} \pi r^2 sin(\theta) d\theta [/tex]

if one just added up cones with the side of the cone being the function [tex]f(\theta)[/tex]. This method would be similar to shells, but apparently I'm [tex]\frac{2}{3} r [/tex] off.

If anyone could help me understand how to calculate volume I would be eternally grateful.

Thanks for taking the time to read this!

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