Insight 2009 Exam 2 - Question 1 [Image Inc.]

[3Xamz]

Question 1) b)

Equation is y = 2arcsin(.5x-1) for [2<=x<=4] and [0<=y<=pi]

It's rotated about the y-axis to make a bowl.

However, in the solutions they used rotated around the y axis to give the volume.
If you draw this graph (which they have in the question), rotating the function of x^2 would only make this "donut" like shape, now a bowl.
Shouldnt we cut out the middle cylinder like shape and add that to the volume too?

[3Xamz]

I've attached a screenie, it's part B im referring to.

They solutions and mine are identical but I have +4pih at the end to make up for that cylinder in the middle..

http://img138.imageshack.us/img138/2817/89984242.jpg