Monday, June 1, 2009

3D Graphing


Vocab You Need to Know



3D graph- used using three variables instead of two: X,Y and Z

Trace- the cross-intersection of a 3D graph, and they help graph two variable equations in the 3D plane

Lateral Surface Area- area of just sides (not bases)

Total surface area-sum of area of all sides



General formulas for 3D graphs
















Basic Formulas To Keep In Mind

Area of Trapezo
id:
Area Regular Polygon:

Area of Circle:

Midpoint:


Volume of a Sphere:



Surface Area of a Sphere:




Volume of a prism:



Graphing a 2 variable equation in 3D


  • use the trace to sketch the graph of the 2 variable equation


  • stretch the trace in the direction of the missing variable


Graphing a 3 variable equation in 3d



  • find each intercept (x,0,0) (0,y,0) (0,0,z)


  • find the equations for all 3 traces


Finding Intersections


  • can be solved algebraically by substitution:

ex: and










the intersection is a circle



Review Questions:


1. find and label the shape of the xy trace for the equation:




2. write a possible equation for a graph with the following traces:

xy: no intersection

yz: hyberbola

xz: hyperbola


3. describe the intersections between the graphs of the following equations:








Given: a right prism of height 12 with an equilateral triangle base of side length 4.


4. find Lateral Surface Area (LSA)


5. find Total Surface Area (TSA)



6. find the Volume of the prism


7. Find the coordinates of the midpoint of segment AB if A(-5, 8,-3) and B(3, 4, -3)



8. Write the equation of a cylinder with diameter 10 whose xz trace is a circle



9. Write the equation of a plane that passes through the points: A(0,6,0) B(2,0,0) C(0,0,-7)



10. A plane intersects a sphere at a distance of 5 from the centre, the radius of the circle formed is 12. Find:


a. the radius of the sphere


b. the surface area of the sphere


c. the volume of the sphere




Answers:



1. ellipse


2. xy: no intersection DNE


yz: hyperbola


xz: hyperbola


final: (2cups)


3. cirlce


4. LSA:

5. TSA:

6.Volume:


7. (-1, 6, -3)


8.diameter= 10, so radius=5









9. given x, y, z intercepts for plane






10. a. radius:



special right triangle 5,12, 13



r=13



b. surface area:
=




c.volume:








5 comments:

Kate Nowak said...

Great start! Were you able to find a way to render 3D graphs?

Kate Nowak said...

It would be helpful if you said what general shape the "general equations" were, i.e. "sphere", "tube", "bowl" (paraboloid), etc.

Ellen + Kelsey said...

yea I actually did it on a separate sheet of paper (drew the sphere, parabloid, haystack, and cups) so that we can scan it later

kelseyyyy said...

Hi! I love your diagrams and this really helped. I still am a little bad at traces but i am much better than where i started! thank you!

burak said...

thank you..