# Modifiable Solid: Rectangular Cross Sections Parallel to yAxis

- Author:
- Tim Brzezinski

- Topic:
- Calculus, Geometry, Integral Calculus, Prism

## HOW TO USE:

Enter any

**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**rectangles**. One side of this**rectangle**(the base) has length = upper(x) - lower(x). The other side (height) of this**rectangle**has length = w * (upper(x) - lower(x)). Thus, the height of any rectangular cross section = w * its base length. You can alter the value of**w**using the (vertical)**w slider**. You can move this**rectangle**by sliding the**MoveMe**slider OR by dragging the**WHITE POINT**along the xAxis. 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**mhnnfubg**(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, w, MoveMe, and Filling**. (Be sure to leave everything else alone.)