# Modifiable Solid: Rectangular Cross Sections Parallel to yAxis

## 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.)