Link to Geogebra 3D sample file]

https://www.geogebra.org/calculator/vxpkrvgv

 

 Attachments

1.         All balloon design material: Graph of balloon, spread sheet, etc.

2.         Printout of the 2-D graph of the equation of your balloon using Desmos or other software

3.         Printout of the 3-D graph of the balloon with varying views.

4.         Printout of the computer numeric solution to your equation for both volume and surface area using Geogebra or other software.  Include a calculation showing the ratio of surface area to volume.

5.         Other supporting material including this handout as the cover page.

 Online resources:

 http://polynomialregression.drque.net/online.php  regression equation and its graph. Like using the TI83 but better. You can cut and copy this equation into other websites or programs. You will need to fix the exponents of variable using the notation x^3 etc.

 

http://www.shodor.org/interactivate/activities/FunctionRevolution/

1. Set the window size to view your balloon.

2. Copy the regression equation into the function box. (leave g(x) blank)

3. Set options to taste and do a screen capture at a few angles.

 

https://www.emathhelp.net/calculators/calculus-2/area-of-surface-of-revolution-calculator/ Surface Area

 

https://www.geogebra.org   a) Notation: Integral (f(x),a,b).

b) For 3-D graph use 3-D Calculator (see figure below)

(Set global rounding higher: Settings>Settings>rounding)

Notation: Surface(f,n,xAxis)

 

 https://www.desmos.com/      Volume and Surface Area with 2-D graph.

More Desmos: https://www.desmos.com/3d/k0zwuszxts

 Derivative as the graph of a function

 https://www.geogebra.org/m/XA6tcnxYPolynomials

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