ATAR Notes: Forum

HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Advanced => Topic started by: Jefferson on March 16, 2019, 04:59:51 pm

Title: Solids of Revolution
Post by: Jefferson on March 16, 2019, 04:59:51 pm
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.



Title: Re: Solids of Revolution
Post by: david.ko3 on March 16, 2019, 10:22:37 pm
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  :'(
Title: Re: Solids of Revolution
Post by: 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
Title: Re: Solids of Revolution
Post by: Jefferson on March 17, 2019, 11:18:15 am

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  :'(

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

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.
Title: Re: Solids of Revolution
Post by: jamonwindeyer on March 17, 2019, 02:43:49 pm
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.

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