Solids with Various Cross Sections: AR Templates
- Tim Brzezinski
- Integral Calculus
Here, we can create various solids formed by stacking prisms (with varying cross-sectional bases parallel to the yAxis) from x = a to x = b. (Ex: see pic below). We form such a solid by stacking prisms of width = dx & where . 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.
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