# Custom Solid: Elliptical Cross Sections Parallel to yAxis

- Author:
- Tim Brzezinski

- Topic:
- Calculus, Ellipse, Geometry, Integral Calculus

## HOW TO USE:

Enter any .
You can move this

**UPPER FUNCTION**(labeled upper(x)). Enter any**LOWER FUNCTION**(labeled lower(x)). Enter your**lower and upper limits of integration**("a" and "b", respectively). Slide the**FILLING**slider all the way to the left. For this solid, note how cross sections parallel to the yAxis are**ellipses**with its entire minor axis lying in the base. This minor axis is parallel to the yAxis and has length = upper(x) - lower(x). In addition, you can alter the eccentricity of this ellipse by using the**ecc**slider. Here**ellipse**by sliding the**MoveMe**slider. You can modify any of these parameters (functions, limits) at any time.**To explore in augmented reality, see the directions below this applet.**## TO EXPLORE IN AUGMENTED REALITY:

1) Open up GeoGebra 3D app on your device.
2) Go to the MENU (horizontal bars) in the upper left corner. Select OPEN.
In the Search GeoGebra Resources input box, type

**m2hgzcyr**(Note this is the resource ID = last 8 digits of the URL for this resource.) 3) In the resource that uploads, zoom in/out if needed. You can alter the functions upper(x), lower(x). You can also move sliders a, b, MoveMe, Filling, and ecc. (Be sure to leave everything else alone.)