# Thread: volume of solid without f(x)

1. ## volume of solid without f(x)

How would you find the volume of a solid rotating about y-axis if you were not given f(x)?, or better yet, how would you come up with the equation of f(x)?

2. You could use various points(x and y coordinates)and implement the proper regression analysis to find an equation. Then revolve.

There are linear regressions, cubic regressions, quartic and quintic regressions, exponential, etc.

A lot of the calculators do these analyses.

For example, suppose we had x values, respectively, of 0,1,2,3,4

y values of 0,2,5,7,11

I ran these through my calculator and got an equation of

$\displaystyle y=\frac{5}{24}x^{4}-\frac{19}{12}x^{3}+\frac{91}{24}x^{2}-\frac{5}{12}x$

Hope this helps a little.

3. ohh ok,

how would I enter values into my TI-83 to find an equation?

or does it only work with TI-89

I mean, I know how to plot the data, but i'm not sure if TI-83 is capable of producing an equation.
If not, how would I derive an equation based on the x,y values?

4. You need some sort of tech to derive the equation. Even a simple linear regression is rather cumbersome, let alone anything higher. I don't know if an 83 will do it or not. I use a Voyage 200 and a TI-92. They certainly do. The 89 will. If you have Excel, it will do it.

If you can gain access to an 89 or Excel, let me know and I can show you the steps.

5. Originally Posted by ch2kb0x
ohh ok,

how would I enter values into my TI-83 to find an equation?

or does it only work with TI-89

I mean, I know how to plot the data, but i'm not sure if TI-83 is capable of producing an equation.
If not, how would I derive an equation based on the x,y values?
I've done galactus' example with a TI83.

1. Store the x-values into list L1
2. Store y-values into list L2

3. Use STAT - CALC - 7QuartReg
4. add L1, L2, Y3 (you find the y-variable at VARS - Y-VARS

5. Press ENTER

You'll get the coefficients of quartic function.

6. There ya' go. I wasn't sure if an 83 would or not. Now we know. That is exactly what my Voyage 200 gave me except I converted to fractions to make it look better.

7. thank you so much, both of you. thanks.