# Thread: Very Quick Question Regarding Surface Area of Revolution (Integration)

1. ## Very Quick Question Regarding Surface Area of Revolution (Integration)

An artist is designing a wine glass in a flower shape, which can be generated by rotating y= sqrt(x) and x= y, between x= 0 and x= 1, about the x-axis. What is the surface area (which contains both the inside and the outside surfaces) of such a glass?

Alright, quick question: until now, I've dealt with Surface Integral problems that involved only one function [for instance, y= sqrt(x)], so inputing 'y' into the surface area formula [2 π y ds] hasn't been a problem. BUT, this one involves two [y= x and y= sqrt(x)] functions. So, my question is, how do I set it up, i.e. how do I enter them into the formula?

2. ## Re: Very Quick Question Regarding Surface Area of Revolution (Integration)

Originally Posted by bhaktir
An artist is designing a wine glass in a flower shape, which can be generated by rotating y= sqrt(x) and x= y, between x= 0 and x= 1, about the x-axis. What is the surface area (which contains both the inside and the outside surfaces) of such a glass?

Alright, quick question: until now, I've dealt with Surface Integral problems that involved only one function [for instance, y= sqrt(x)], so inputing 'y' into the surface area formula [2 π y ds] hasn't been a problem. BUT, this one involves two [y= x and y= sqrt(x)] functions. So, my question is, how do I set it up, i.e. how do I enter them into the formula?

The inside surface is a cone, you should know the formula for surface area of a cone. So you really only have to evaluate one surface integral (for the outside).

3. ## Re: Very Quick Question Regarding Surface Area of Revolution (Integration)

But, how would you set up this problem?

I'm sorry but I still don't understand this.

4. ## Re: Very Quick Question Regarding Surface Area of Revolution (Integration)

Originally Posted by bhaktir
But, how would you set up this problem?

I'm sorry but I still don't understand this.
You said you know how to evaluate a surface area when you only have one function. Like I said, you only need to integrate one function (the square root) for the surface area of the outside of the glass, because the inside is a cone, which you should already be able to evaluate without integration.

5. ## Re: Very Quick Question Regarding Surface Area of Revolution (Integration)

All I know is the formula (2 π y ds). I really don't know the rest. If you could just show me how to set this problem up, I'd be extremely grateful. Thanks!

6. ## Re: Very Quick Question Regarding Surface Area of Revolution (Integration)

Never mind, I got it.

For future reference, the cone formula isn't necessary in attaining the answer.

Thanks for the help!

7. ## Re: Very Quick Question Regarding Surface Area of Revolution (Integration)

Originally Posted by bhaktir
Never mind, I got it.

For future reference, the cone formula isn't necessary in attaining the answer.

Thanks for the help!
It is if you want the inner surface area as well...