2002 AP calculus free response -- areas and volumes

See www.midnighttutor.com for all of our calculus tutorials. Tutorial of how to solve this problem from the 2002 AP AB test involving volumes of revolution and based on crosssectional area.

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Howto & Style

Tags:

• calculus
• tutorial
• revolution
• volume
• area
• integration
• integral

[voiyour]

Here's my Q... You said something like, "you could solve this algebraically in a million years." I wonder, since Newton invented calculus around 1700, how did they do this in the pre graphing calculator days?

[tcbeez]

hahaha are you kidding!!! it gets so much harder than calculus SOOOOO much harder shit that will blow your mind!

[MrAlienpirate]

sometimes you can make them equal to eah other, rearrange to make equal to zero, use quadratic formula to find points of intersect then just do the hole intergrate thingy but i dont think it would work for somthing like this i think it only works for area

[iTr4nC3]

great video it helped alot, but where is the solve button that i can use to store my intersect x value, i know how to solve numbers when i type them in, but idk how to from a graph.

[gf2468]

if compare to malaysia SPM Additional mathematics can be say like a kid face a God!

[VeggiePirateLorryn]

Those are the same answers.

His area is just rounded to the third digit after the decimal.

And his volume is 10.149 times pi.

Which equals your volume.

[chukivano]

No, actually, Calculus is the hardest math. I asked somebody.

[MoogSound]

AP Calculus is easy as hell for me...i dont know if there is anything harder than that is there?

[Ebag1990]

Also for part C I don't see any answer either so I'd like someone to check on mine as this is the part I'm usually really bad at.

Volumed of R using square cross sections: 8.997003873

[Ebag1990]

I'm not sure whether or not this is right or not but here are the answers I got. Somebody respond and tell me if mine are right because the guy below me got slightly different answers.

Area: 3.214564711

Volume: 31.88486997

[JunoK1]

sorry to repost but checking answers-

Area=3.215

Volume=10.149*(Pi)