Volume of Revolution - 3d object

Question

Recently we were given an assignment in which we have to model the cross-section of a 3d, symmetrical object utilising functions. Then we must find the volume of revolution of the object. I need ideas of what i can do. I thought of creating a groovy candle holder, but it has many repeating shapes and curves. This would make the calculations and explanations in my report repetitive and boring. Some suggestions were flower vases, drink bottles. The object must be made up of at least 2 seperate parts which join to create the object. The shape must be relatively complex. Also, the shape must be hollow at at least one section. Be creative.

Answer 1

You should be able to create a horn 3D shape by rotating a section of the $y=\frac{2}{x}$ curve around the $x$-axis. You can make it hollow by removing the inner volume created by another similar curve, let's say, $y = \frac{1}{10} + \frac{2}{x}$:

You could also add more details to the horn, like buttons or handles, by rotating other lines or curves.

Answer 2

One way would be to use the area and the centroid of each part , filled or empty, of the cross section and then use the formula $$V=A 2 \pi r$$ to find the volume of revolution.

Volume of helycoidal grooves / bumpings are also easy to find by this method.