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blackstreet23
 one year ago
What was the calculus formula to determine the volume of a solid? I don't mean solid of revolution. Just regular solid.
blackstreet23
 one year ago
What was the calculus formula to determine the volume of a solid? I don't mean solid of revolution. Just regular solid.

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blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0volumes of cross sections

freckles
 one year ago
Best ResponseYou've already chosen the best response.3Are you sure you aren't looking for: \[\text{ Volume }=\int\limits_a^bA(x) dx \text{ where } A(x) \text{ is the area of the cross section } ?\]

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0yes that is it ! thank you !

freckles
 one year ago
Best ResponseYou've already chosen the best response.3that's also the formula used in solids formed by revolution of some curve about some axis

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1u forget to square it..i think @freckles

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you know where we take circles as the cross section

freckles
 one year ago
Best ResponseYou've already chosen the best response.3no A(x) is the area you don't want to square the area

freckles
 one year ago
Best ResponseYou've already chosen the best response.3if the cross section is a circle then A(x)=pi*r^2

freckles
 one year ago
Best ResponseYou've already chosen the best response.3where r is a function of x

freckles
 one year ago
Best ResponseYou've already chosen the best response.3though we could look at things in terms of y too not just x

freckles
 one year ago
Best ResponseYou've already chosen the best response.3you know depending on what suits us better

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0but how is that the formula for solids of revolution? I mean the formula for solids of revolution is \[\int\limits_{a}^{b}(\pi*f(x)^2) dx\]

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1i think the f(x) is actually the radius

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0f(x) is the function

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0i mean the height of the funtion

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1yes which is intern the radius so A=pi*r^2

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1and freckles just use the Area instead...i think

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0I guess i am kind of confuse lol

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1ok lets wait on till @freckles come online...

freckles
 one year ago
Best ResponseYou've already chosen the best response.3area of a circle is what I called A(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3or the are of the cross section is A(x)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3if the cross section is a circle then A(x) is pi*r^2 where r is the radius f(x) is the distance from the curve to the xaxis so f(x) is the radius if the axis of rotation is the xaxis

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440894543729:dw Say we want to take this curve on [a,b] and rotate it about the xaxis

freckles
 one year ago
Best ResponseYou've already chosen the best response.3first reflecting the curve about the xaxis gives us: dw:1440894612771:dw now that drawing is not that great but that curve is basically suppose to be a mirror for the other curve I drew

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440894662165:dw so we have a cross section that is a circle

freckles
 one year ago
Best ResponseYou've already chosen the best response.3notice the distance from the xaxis to the curve is indeed the radius which is called f(x) in this case

freckles
 one year ago
Best ResponseYou've already chosen the best response.3\[\int\limits_{a}^{b}A(x) dx \\ \text{ so we have } A(x)=\pi \cdot (f(x))^2 \\ \]

LynFran
 one year ago
Best ResponseYou've already chosen the best response.1so i was right about f(x) being the radius?

freckles
 one year ago
Best ResponseYou've already chosen the best response.3dw:1440894830121:dw yes

freckles
 one year ago
Best ResponseYou've already chosen the best response.3but the A(x) is not squared

freckles
 one year ago
Best ResponseYou've already chosen the best response.3A(x) just means area of the cross section

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0ohh i see ! I thought f(x) was just the height of the function

blackstreet23
 one year ago
Best ResponseYou've already chosen the best response.0It makes so much sense now :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.3well you can also say f(x) is the height of the function

freckles
 one year ago
Best ResponseYou've already chosen the best response.3I put   around it because f(x) could happen to be negative which just means the height is below the xaxis
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