# Solids with Various Cross Sections: AR Templates

- Author:
- Tim Brzezinski

- Topic:
- Integral Calculus

## CALCULUS STUDENTS:

Here, we can create various solids formed by stacking prisms (with varying cross-sectional bases parallel to the yAxis) from .
a = lower limit of integration (modifiable via slider)
b = upper limit of integration (also modifiable via slider)
n = number of prisms with height = dx. This is also modifiable by using the n slider.
You can also change
f(x) = upper (greater) function
g(x) = lower (lesser) function
For each of these demos (shown below), the upper function is , and the lower function is . In these demos, a = -8 & b = 8.

*x*= a to*x*= b. (Ex: see pic below). We form such a solid by stacking prisms of width = dx & where## Ex:

## HOW TO EXPLORE:

**Directions:**1) Open up GeoGebra 3D app on your device. 2) Click on the 3 horizontal bars (upper left corner). Select

**OPEN**. For cross sections parallel to the yAxis that are...

**EQUILATERAL TRIANGLES**(where f(x) - g(x) = one side), type this code:

**XArpgR3A**

**SQUARES**(where f(x) - g(x) = one side), type this code:

**y7mnphxm**

**ISOSCELES RIGHT TRIANGLES**(where f(x) - g(x) = LEG), type this code:

**shks2q7v**

**REGULAR PENTAGONS**(where f(x) - g(x) = one side), type this code:

**zmhqnrqb**

**SEMICIRCLES**(with diameter = f(x) - g(x)), type this code:

**cygnvepm**