Question 1

Use the Theorem of Pappus to find the volume of the solid generated when the region bounded by the x-axis and the semicircle y= sqrt(a^2 -x^2) is revolved about

a) the line y=-a

b) the line y=x-a

Question 2

Use the Theorem of Pappus to find the centroid of the triangular region with vertices (0,0), (a,0), and (0,b) , where a> 0 and b>0 .

Hint Revolve the region about the x-axis to obtain y bar and about the y-axis to obtain x bar.

I don't quite understand the Pappus theorem. Please do help you know how to solve them. Thank you very much.