AP calc AB- Volumes

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Discus: SAT/ACT Tests and Test Preparation: April 2004 Archive: AP calc AB- Volumes
By Becks777 (Becks777) on Sunday, April 25, 2004 - 10:10 pm: Edit

I seem to be having a lot of trouble with the last chapter in AP calc- Finding VOLUMES. Can someone tell em when to use shells and when to use disks. Also how to find volumes using shells?

By Geoff912 (Geoff912) on Sunday, April 25, 2004 - 10:37 pm: Edit

ok you use disc method when your rotating around something horizontal and shell when your rotating around something vertical....
Disc must be in terms of x(y=)
Shell must be in terms of y(x=)

By Justice (Justice) on Monday, April 26, 2004 - 01:04 am: Edit

That's not really true geoff...

Use shells if the disk method requires the solving of a function in terms of an unsolvable variable, ie. y = 4x^3 + x. It allows you to circumvent that need to rotating on a different axis.

By Jason817 (Jason817) on Monday, April 26, 2004 - 02:13 am: Edit

volumes of revolutions...easily the hardest thing about calc AB.

By Ubercollegeman (Ubercollegeman) on Monday, April 26, 2004 - 03:09 am: Edit

Volume isn't too tough if you understand the concept.

Basically, I don't like to involve shells unless I have to. How can you tell?

a. y is not solvable in x or vice versa.
b. The function's disk radius behaves funny.

I always check to see if disks/washers will work first. It's all really just about visualization skills. If you can picture the graph revolving around the axis, you're home free.

By Becks777 (Becks777) on Monday, April 26, 2004 - 02:45 pm: Edit

How do you use shells. I mean how do you find the radius and the height. Also if you rotate something about the Y-axis, does that mean you have to use shells? If not, how would you work out the problem.

By Justice (Justice) on Monday, April 26, 2004 - 03:12 pm: Edit

the radius will always be either x or y. The height is the function in the same variable. The axis on which you rotate makes no difference. Where did you get that idea? You know that for shells, you're taking a lot of 2pirh, so you integrate that. That's all there is to it.

By Becks777 (Becks777) on Monday, April 26, 2004 - 04:16 pm: Edit

sorry...i have it all messed up right now! the sad part is that my class covered volumes when i was diagnosed with a heavy case of seniorites!

By Becks777 (Becks777) on Monday, April 26, 2004 - 09:35 pm: Edit

OK how would someone do this question:
If the region enclosed by the y axis, the line y=2, and the curve y=Sq rt( X)is revolved about the y axis, the volume of the solid generated is ??

By Jshifton (Jshifton) on Monday, April 26, 2004 - 10:46 pm: Edit

First take out your calculadora, and graph Y=2 and Y=Sqrt(X). This should give you a good visualization of the task at hand.

If you look at the graph, it seems easiest to integrate with respect to X. Therefore, since dx is perpendicular to the axis of rotation (the Y-axis), you are taking shells.

The equation for shell volume is dV= (Circumference)(Altitude)(dx or dy). Therefore we have dV= (2PiX)(2-Sqrt(x))dX

Now calculate the bounds. Since the problem tells us the Y-axis, we know the first bound is 0. For the second bound, solve for when the Sqrt(x) is equal to 2. This is 4.

Enter your dV equation into Y1 of your calculator, then enter the command Fnint(Y1,X,0,4)

This is your answer. I got 20.106 cubic units.

By Andrew123s (Andrew123s) on Monday, April 26, 2004 - 11:48 pm: Edit

Aren't shells not even on the AP test?

By Ubercollegeman (Ubercollegeman) on Monday, April 26, 2004 - 11:56 pm: Edit

The radius is NOT always x or y. The radius is only x or y if the axis of revolution is either the y-axis or the x-axis (respectively). Radius is going to be the distance from the axis for that shell.

By Aim78 (Aim78) on Tuesday, April 27, 2004 - 01:50 am: Edit

Never heard of any of this. What a joke class.

By Impatheticiknow (Impatheticiknow) on Wednesday, April 28, 2004 - 06:51 pm: Edit

Volumes are not that bad. It is simply a matter of executing an algorithm (although cross sections are much harder than washer/disk). However, I HATE related rates.

By Becks777 (Becks777) on Wednesday, April 28, 2004 - 08:01 pm: Edit

Does anyone have an idea about what percent of the test you need to get right for a 5?

By Gmf05 (Gmf05) on Wednesday, April 28, 2004 - 08:08 pm: Edit

It's somewhere around 80% if you miss the other 20%

By Hypatia67 (Hypatia67) on Thursday, April 29, 2004 - 12:47 am: Edit

The shell method is NOT tested on the AB Calculus test. You only have to know disk/washer method. It might be easier to use the shell method but it is never necessary to solve a problem with it.

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