Help With Volumes (1 Viewer)

[5647382910]

Im very confused:
why is it that when u find the volume when the curve y = sqrt x is rotated between x = 0 and x = 4 around the y-axis you have to do: volume of cylinder with radius 4 and height 2 - S(from y=2 to y=0)of y^4 dy;
How come u cant just do S(from y=2 to y=0)of y^4 dy

 

[tommykins]

回复: Help With Volumes

Uh, the area between the cureve y = sqrtx and x=0,x=4 rotated around the y axis isn't a cylinder? :S

 

[lyounamu]

Im very confused:
why is it that when u find the volume when the curve y = sqrt x is rotated between x = 0 and x = 4 around the y-axis you have to do: volume of cylinder with radius 4 and height 2 - S(from y=2 to y=0)of y^4 dy;
How come u cant just do S(from y=2 to y=0)of y^4 dy

You sure you are not finding something else?

Post up the question.

 

[5647382910]

Re: 回复: Help With Volumes

Uh, the area between the cureve y = sqrtx and x=0,x=4 rotated around the y axis isn't a cylinder? :S

I know... its a curved cone looking thing but in order to get this u have to do the volume of the cylinder from x = 4 to x = -4 - the integral i wrote;
i dont know y... but im 100% sure thats the way u do it

 

[5647382910]

You sure you are not finding something else?

Post up the question.

it was in one of the JRAHS papers... i think it read: the area between the curve y = sqrt x between y = 2 and y = 0 is rotated about the y axis; find the volume of revolution

 

[tacogym27101990]

are you finding the volume enclosed by the graph
of y=sqrtx and the x axis when its rotated around the y axis between x=o and x=4?
because then you would have to do it a different way

 

[5647382910]

are you finding the volume enclosed by the graph
of y=sqrtx and the x axis when its rotated around the y axis between x=o and x=4?
because then you would have to do it a different way

no, the area between the curve and the y axis between y = 2 and y=4

 

[tacogym27101990]

then its just
V= pi S y^4dy from y=0 to y=2

 

[5647382910]

then its just
V= pi S y^4dy from y=0 to y=2

thats wat i thoguht as well but its not... by doing that were finding the volume of the curve between the x axis rotated around the y-axis; i know this sounds weird but im 100% sure that you have to minus that volume from the cylinder from x = -4 to x = 4 with height 2

 

[tacogym27101990]

thats wat i thoguht as well but its not... by doing that were finding the volume of the curve between the x axis rotated around the y-axis; i know this sounds weird but im 100% sure that you have to minus that volume from the cylinder from x = -4 to x = 4 with height 2

no sorry mate your 100% wrong
have you ever derive the volume formulas, because if you havent, i doubt very much you understand it.

 

[5647382910]

no sorry mate your 100% wrong
have you ever derive the volume formulas, because if you havent, i doubt very much you understand it.

OK... if u insist... i dnt think we are thinkn g of the same thing... wat about: find the volme of revoluron when the the area between the curve y = x^2 and x = 0 and x = 4 is rotated around the x axis

 

[tacogym27101990]

OK... if u insist... i dnt think we are thinkn g of the same thing... wat about: find the volme of revoluron when the the area between the curve y = x^2 and x = 0 and x = 4 is rotated around the x axis

well yes then in two unit you would have to find the volume of the cylinder then subtract the volume when the curve is rotated around the y-axis.

but in four unit, you learn a much quicker, funner way

 

[5647382910]

well yes then in two unit you would have to find the volume of the cylinder then subtract the volume when the curve is rotated around the y-axis.

but in four unit, you learn a much quicker, funner way

ok, but can i ask why? How come u just cant do the integral and not suntract; what makes this cas different frmt he others

 

[shaon0]

well yes then in two unit you would have to find the volume of the cylinder then subtract the volume when the curve is rotated around the y-axis.

but in four unit, you learn a much quicker, funner way

is the 4unit way using cylindrical shells or something?

 

[tacogym27101990]

ok, but can i ask why? How come u just cant do the integral and not suntract; what makes this cas different frmt he others

ok well the theory behind taking volumes is that we take really thin slices (dy) of the revolved curve. by summing those slices we can find the volume
if the curve is rotated around the y-axis, to find the volume between the y-axis and the curve, each slice will represent a circle radius of x, and the area of the circle is pix^2, so the total volume is piSx^2dy

but when we find the volume between the curve and x-axis, each slice will represent an annulus, so we have to derive a new formula as there will be a hole in the middle of the solid

 

[tommykins]

回复: Re: Help With Volumes

Ya.

 

[tacogym27101990]

is the 4unit way using cylindrical shells or something?

yeah you can do it by cylindrical shells, or sometimes just using annulus discs.
i prefer the shells method

 

[tommykins]

回复: Re: Help With Volumes

Shells is the best, seriously.

 

[tacogym27101990]

Re: 回复: Re: Help With Volumes

Shells is the best, seriously.

it really is aye.
volumes and integration would have to be my favourite topics.

 

[shaon0]

yeah you can do it by cylindrical shells, or sometimes just using annulus discs.
i prefer the shells method

yeah i don't like the annulus disc method in certain cases where i can choose