Volumes Question (1 Viewer)

[~ ReNcH ~]

From my recent Volumes exam:

The curve y=sinx is revolved about the line y=1. Use an appropriate slicing technique to find the volume of the solid of revolution formed by the portion of the curve from x=0 to x=pi/2.

Does this question imply that the volume is formed by rotating the area bounded by the curve y=sinx, x=0, x=pi/2 and the x-axis around the line y=1? Or is the volume obtained by rotating the area bounded by y=sin, x=0, x=pi/2 and the y-axis around the line y=1?

 

[polythenepam]

well it should specify shouldnt it?
cos it could be either way just as likely

 

[~ ReNcH ~]

That was the way it was presented in the exam, and having got it back yesterday (yes, I had to go to school yesterday ), the solutions illustrated the volume as being bounded by the y-axis. In the exam, I calculated the volume as being the area bouded by the x-axis rotated around y=1 and I think I lost 2 marks for that (I didn't get my paper back, only my mark). I personally thought the question was a bit ambiguous, but I haven't had the chance to debate it with my teacher yet.

 

[polythenepam]

hmm yeeh so ur sure it didnt specify at all?
maybe when they mentioned slicing they intended that to imply it being bound by the y-axis.. n im assuming u used the washer method.. although the washer method is a type of slicing method isnt it? hmm.. ohh well.. if they didnt specify then u hav the right to scab ur marks back.. good luck

 

[~ ReNcH ~]

Nope...the question didn't specify at all - I typed the question directly from the exam paper.
I used annular slices to calculate the volume as you said, and to my knowledge that's a valid "slicing" technique.

 

[who_loves_maths]

Originally Posted by ~Rench~
From my recent Volumes exam:

The curve y=sinx is revolved about the line y=1. Use an appropriate slicing technique to find the volume of the solid of revolution formed by the portion of the curve from x=0 to x=pi/2.

Does this question imply that the volume is formed by rotating the area bounded by the curve y=sinx, x=0, x=pi/2 and the x-axis around the line y=1? Or is the volume obtained by rotating the area bounded by y=sin, x=0, x=pi/2 and the y-axis around the line y=1?

don't be mad at me for saying this ~Rench~, but the volume required is CLEARLY that bounded by the y-axis.

why? take a look at what you have typed:
"Does this question imply that the volume is formed by rotating the area bounded by the curve y=sinx, x=0, x=pi/2 and the ... ?"

do you realise that the line x=0 IS the y-axis ???

also, it wouldn't make sense if it was the x-axis, since the question does not specify and so there is an INFINITE amount of AREA between x=0 and x=1 BENEATH the curve y=sin(x).
ie. why stop at the x-axis? why not go lower, eg. enclosed by the horizontal line y= -1000000..... ? the only thing special about the x-axis is that its a standard coordinate axis, otherwise its just a line with the equation y=0 .

i hope you get what i'm saying here... it just won't make logical sense to ASSUME that its the x-axis... but its clear that the question has specified that it is bounded by the y-axis, since x=0 is the y-axis itself.

hope you understand now

 

[~ ReNcH ~]

Now that's just confirmed my stupidity
I wrongly assumed that the area was bounded by the x-axis. My mistake.
Thanks for clearing that up

Edit: And no, of course I'm not mad at you. I'm grateful that you clarified my misunderstanding of the question, or else I'd only do it again in the trial or worse, in the HSC exam.

 

[who_loves_maths]

^ haha... okay, well i'm glad to be of help :uhhuh: