Calc II Y = (a^2 - x^2)^(1/2)

[calc II]

?Find the surface area when Y = (a^2 - x^2)^(1/2) is revolved around the x-axis?

?Geometrically, what have you found?

Please help. Thank you.

 

[Char. Limit]

Could you show us what you have tried? It might give us an idea on where you need help.

Also, there is a template for homework posts. For future reference, please use it. It should appear by default whenever you start a new topic in the homework section.

 

[calc II]

Could you show us what you have tried? It might give us an idea on where you need help.

Also, there is a template for homework posts. For future reference, please use it. It should appear by default whenever you start a new topic in the homework section.

I just need help on how to set up the problem. (And i'll definitely use the template next time)

 

[Char. Limit]

Well, firstly, how well do you know arc length? Because it will be needed here...

And tell me, how would you find the surface area of a regular solid, like say a cylinder, that has no top or bottom to consider?

Your equation in a more elegant format:

$$y=\sqrt{a^2-x^2}$$

 

[rs1n]

?Find the surface area when Y = (a^2 - x^2)^(1/2) is revolved around the x-axis?

?Geometrically, what have you found?

Please help. Thank you.

Your equation $$y=\sqrt{a^2-x^2}$$ may be more recognizable in the form $y^2+x^2=a^2$. What shape does the graph of this equation have? Can you deduce how $$y=\sqrt{a^2-x^2}$$ relates to $y^2+x^2=a^2$? This should help with the second question (and also give you an idea of what to expect for the answer to the first question). As Char.Limit pointed out, a good look at the arc length and surface area formulas might be in order.