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I apologize if this question is obvious or simple. ImI'm in HighSchoolhigh school and have started playing around with MathmaticaMathematica only recently.

For my Calculus Final, I am supposesupposed to use rotation about the y axis$y$-axis to determine the volume of a bundtBundt cake.

I took a slice of the cake, put it on graph paper, recreated it in Photoshop, and manually extracted data points.

Both axisaxes are in inches with each interval of 1 inch.

enter image description hereBundt cross section

Here is a google sheetsGoogle Sheet with the data.

I cut out the data points that allowed the top half of the curve to be a function and fit a quadratic function. Rotating that funtion gave me a volume. However the volume of the quad. func.quadratic function is larger than the true volume because of the overshot area.

I believe fitting parametric curves and their rotation will result in the most accurate value for the volume.

However being an absolute MathmaticaMathematica beginner, I have no idea how to fit a parametric curve to this data.

Any help would be much appreciated.

Edit: I ran into this article which somewhat gets to what imI'm trying to dodo; however, it deals with much much more complicated functions.

I apologize if this question is obvious or simple. Im in HighSchool and have started playing around with Mathmatica only recently.

For my Calculus Final I am suppose to use rotation about the y axis to determine the volume of a bundt cake.

I took a slice of the cake, put it on graph paper, recreated in Photoshop, and manually extracted data points.

Both axis are in inches with each interval of 1 inch.

enter image description here

Here is a google sheets with the data.

I cut out the data points that allowed the top half of the curve to be a function and fit a quadratic function. Rotating that funtion gave me a volume. However the volume of the quad. func. is larger than the true volume because of the overshot area.

I believe fitting parametric curves and their rotation will result in the most accurate value for the volume.

However being an absolute Mathmatica beginner I have no idea how to fit a parametric to this data.

Any help would be much appreciated.

Edit: I ran into this article which somewhat gets to what im trying to do however it deals with much much more complicated functions.

I apologize if this question is obvious or simple. I'm in high school and have started playing around with Mathematica only recently.

For my Calculus Final, I am supposed to use rotation about the $y$-axis to determine the volume of a Bundt cake.

I took a slice of the cake, put it on graph paper, recreated it in Photoshop, and manually extracted data points.

Both axes are in inches with each interval of 1 inch.

Bundt cross section

Here is a Google Sheet with the data.

I cut out the data points that allowed the top half of the curve to be a function and fit a quadratic function. Rotating that funtion gave me a volume. However the volume of the quadratic function is larger than the true volume because of the overshot area.

I believe fitting parametric curves and their rotation will result in the most accurate value for the volume.

However being an absolute Mathematica beginner, I have no idea how to fit a parametric curve to this data.

Any help would be much appreciated.

Edit: I ran into this article which somewhat gets to what I'm trying to do; however, it deals with much more complicated functions.

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Fitting a Parametric Curve

I apologize if this question is obvious or simple. Im in HighSchool and have started playing around with Mathmatica only recently.

For my Calculus Final I am suppose to use rotation about the y axis to determine the volume of a bundt cake.

I took a slice of the cake, put it on graph paper, recreated in Photoshop, and manually extracted data points.

Both axis are in inches with each interval of 1 inch.

enter image description here

Here is a google sheets with the data.

I cut out the data points that allowed the top half of the curve to be a function and fit a quadratic function. Rotating that funtion gave me a volume. However the volume of the quad. func. is larger than the true volume because of the overshot area.

I believe fitting parametric curves and their rotation will result in the most accurate value for the volume.

However being an absolute Mathmatica beginner I have no idea how to fit a parametric to this data.

Any help would be much appreciated.

Edit: I ran into this article which somewhat gets to what im trying to do however it deals with much much more complicated functions.