Finding Volume and Surface Area of a Banana Using Calculus

[TKDonuts]

Homework Statement

We are given a Banana, and asked to find the volume and surface area of the function, using calculus. So far, we have learned elementary calculus (derivatives, limits, and integrals) as well as volumes of revolutions. We traced the banana on graph paper, plotted points on the line, and created equations for the cross section of the banana. Here is the graph on desmos: https://www.desmos.com/calculator/jfertkhwnv
We measured the actual volume of the banana, using a water displacement method. The actual volume of the banana is 160cm^3

Homework Equations

We are allowed to use any credible resource for equations online.

The Attempt at a Solution

So far, what we have tried is to find the integral between the two lines we traces, (the integral from one end to the other end of the banana, of f(x)-g(x).)(couldn't figure out how to put integral sign in thing.) We then multiplied that value by 1/2, to find the approximate radius. then the calculated radius was plugged into pi*r^2 equation, and we got a value that was incredibly high. Perhaps our equations were incorrect, but at this point, we do not know. We also need to find a method to find the surface area of the banana, however we have not started that phase of the project.

 

[LCKurtz]

For what it's worth, using your equations and assuming circular cross section for the banana I get a volume of a bit over $286$ cubic units.