Our plan was to see if we could figure out the volume of a Pom Wonderful bottle using revolutions around the x-axis. We would wrap string around the bottle to find the circumference and use that to find the radius. Next we would graph those points to find an equation that matched them. Finally we would use some calculus to find the volume and see if we were close. Our goal was to get as close to 355 mL as possible.
This is to help visualize how we turn a simple graph into a 3D model by rotating it around the x-axis.
We then used integrated the equations to find a volume of 393 mL, a 10% error from the measured 355 mL. The error is due to human error, the odd shape of the bottle making it hard to measure, and that our functions don’t 100% match the points.
If you want to play around with your own solids or revolution click here.