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Solids of Revolution

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Jefferson :
Hi everyone,

For this question, I broke the function into 2 curves and have the larger volume subtract the smaller.
I can't seem to get the answers provided by the textbook, which is 215pi/6 u^3.

Please show me how this question should be done.
Thank you.

david.ko3:
Hey!!  ;D I am not sure if your answer is correct or not but I can tell you how the text book obtained their answer.
The text book only used the "Right side" of the graph:

Which results in:

And then what the answers go toward is that:

This results in:

which gives the final number of:

However, we forgot to multiply the pi so we get:

I am not sure this helped a lot but I hope it at least tells you what the answers did!!! Sorry if it didn't help  :'(

jamonwindeyer:
Hey! Thanks heaps to David for the working above ;D assuming that's what the textbook has done, they've done that because they've wanted you to assume that the volume starts at the y-axis and stops as soon as you hit the curve - Which indeed happens on the right hand side of the graph.

That's a bit of an ambiguous thing to ask though, and indeed, the way you've done it Jefferson is way more interesting a question anyway ;D

Jefferson :

--- Quote from: david.ko3 on March 16, 2019, 10:22:37 pm ---
I am not sure this helped a lot but I hope it at least tells you what the answers did!!! Sorry if it didn't help  :'(

--- End quote ---


--- Quote from: jamonwindeyer on March 17, 2019, 10:11:14 am ---Hey! Thanks heaps to David for the working above ;D assuming that's what the textbook has done, they've done that because they've wanted you to assume that the volume starts at the y-axis and stops as soon as you hit the curve - Which indeed happens on the right hand side of the graph.

That's a bit of an ambiguous thing to ask though, and indeed, the way you've done it Jefferson is way more interesting a question anyway ;D

--- End quote ---

Hi,
Thank you both for answering. It did help a lot!
I guess my interpretation of the question was off. Yikes.
Deeply appreciated the worked solution and clarification.
- Jefferson.

jamonwindeyer:

--- Quote from: Jefferson  on March 17, 2019, 11:18:15 am ---Hi,
Thank you both for answering. It did help a lot!
I guess my interpretation of the question was off. Yikes.
Deeply appreciated the worked solution and clarification.
- Jefferson.

--- End quote ---

I'd say the question was off, not you! :)

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