Volume and Rotation of a Solid (basic)

Name:         Volume
Author:       Wilson W. Ng   Waesh@yahoo.com
Version:      1.0
Machine:      TI-82, TI-83, and TI-83plus
Released:     April 23, 2002
Description:  Calculates the volume of a solid and displays the general equation after 
		it is rotated across the x-axis, y-axis, x= a real number, and y= some integer
		(useful for those in Cal 1 or 2 who are learning rotation of a solid)


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Instructions
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1)
Go to the graph menu on your calc y(x)=

You can only enter 3 equations max at once for using this program. 

(y1= and y2=) For typing in the 2 equations.

(y3=) For rotation across the x= some whole number and y= some integer.
Nothing needs to be typed here if the solid is rotated across the 
x and y axis.

2)
Exit the graph menu and run the program. Press Enter to continue.

(A= and B=) are the lower and upper limit.

(Top=) You enter 1 for y1 or 2 for y2 depending on which curve is on the top.

(Rotation across what?) Use 1, 2, etc to pick.

(Space between rotation?) If there is a space after the solid is rotated,
pick yes.

By the way, it is easier to draw a sketch of the graphs first then use
that to figure out if there is space between the solid after rotation.

For this program, you need to change your 1st and 2nd equation into the dy format
for rotation across the y-axis and x= some number.

Example: y=x^2 and y=x^(1/2)
change y=x^2 to x=y^(1/2), but you need to type y=x^(1/2) on the graph menu.
change y=x^(1/2) to x=y^2, but you type y=x^2 on the graph menu.


Then you get a value, but you need to times it by pi (3.14) to get the answer of 
the volume. The general equation used to calculate the value is shown on the 
bottom of the screen.


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Examples
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Find the volume of a solid generated by revolving the region bounded
by y=x^(1/2) and the lines y=2 and x=0 about


A) the x-axis.

y1=2	y2=x^(1/2)	A=0	B=4	Top=1	Rotate across x-axis

Yes for space between rotation. You get 8 and times it by pi.


B) the line y=2.

y1=2	y2=x^(1/2)	y3=2	A=0	B=4	Top=1	Rotate across y=?

No space between rotation. You get 8/3 or 2.67 and times it by pi.


C) the y-axis.

y1=x^2	y2=0	A=0	B=2	Top=1	Rotate across y-axis.

No space between rotation. You get 32/5 or 6.4 and times it by pi.


D) the line x=4.

y1=x^2	y2=0	y3=4	A=0	B=2	Top=1	Rotate across x=?

Yes for space between rotation.	You get 224/15 or 14.93 and times it by pi.


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Known Problems
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If you get a negative value, then the general equation used to calculate the 
volume is a little off. You have to switch all the signs in your integrand. 
However, you still get the correct volume even if the the equation is off by 
changing the value from negative to positive. 

There might be some minor problems with the program. This version was ported 
from my 86/85 without testing the program on the 82, 83, and 83 plus. However,
I looked through the texas instrument guidebooks in the programming section of
the 82 and 83plus. If you know a little about basic programming, you can probably
fix the I/O and Ctrl errors.

If you find any more bugs, have any ideas for improvements or just want
to send a comment, please contact me at:
waesh@yahoo.com


DO NOT SEPARATE THIS DOCUMENT FROM THIS PROGRAM!

Copyright (C) 2002 Wilson Ng
