Volumes - CSSA 2008 Paper. (1 Viewer)

[tommykins]

Forgot what question exactly but I'll type it up -

The area bounded by the curve y = sqrt x and y = x/2 is rotated by the x axis. Using the method of cylindrical shells, find it's volume.

 

[munch0r]

oops made mistake :/

 

[tommykins]

method/working out?

or are they expecting us to do shells for y = sqrtx and minus that from shells for y = x/2 ?

 

[munch0r]

method/working out?

or are they expecting us to do shells for y = sqrtx and minus that from shells for y = x/2 ?

answer is 8pi/3 u^3

if you want to do it via shells rotated around the x axis you have to do shells for y=x/2 minus shells for y = sqrtx

V of a shell = 2pi (2y^2 - y^3) dy

Integral from 2 to 0 of 2y^2 - y^3 = 2pi [ 2y^3/3 - y^4/4]

= 2pi(16/3 - 4)
= 8pi/3

 

[tommykins]

Oh, it's that simple?

How'd you get 2y² - y³ ?

 

[munch0r]

Oh, it's that simple?

How'd you get 2y² - y³ ?

volume of a shell = 2 pi x y dy

so for y = x/2
x = 2y
so 2pi (2y^2)dy

and for y = sqrtx
x = y^2
so 2pi (y^3) dy

 

[cccclaire]

oh lol, we had this exact question in our trials.


I, being the excellent 4u maths genius that I am, rotated it around the y axis.

Got a suprising amount of marks considering though...

 

[tommykins]

回复: Re: Volumes - CSSA 2008 Paper.

volume of a shell = 2 pi x y dy

so for y = x/2
x = 2y
so 2pi (2y^2)dy

and for y = sqrtx
x = y^2
so 2pi (y^3) dy

Thank you for that, I think my main problem was trying to make it into one shell

@ccclaire - nice job lah

 

[Poad]

Heh, I remember that question. I actually got a negative answer. >_>

 

[tacogym27101990]

is the answer 8pi/3 u^3??

it was either a really easy question or i got it wrong

 

[midifile]

Heh, I remember that question. I actually got a negative answer. >_>

I did that once in a 3unit test

I just absolute valued it when I was running out of time

 

[munch0r]

is the answer 8pi/3 u^3??

it was either a really easy question or i got it wrong

yes, verified it using slices, got the same answer...

 

[tommykins]

回复: Re: Volumes - CSSA 2008 Paper.

I did that once in a 3unit test

I just absolute valued it when I was running out of time

Same, and i somehow got ful marks xD