# calculus 2: Find the volume of the solid

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$$y = 1 + sec\;x,\;y =3,\;about\;y=1$$

How is the inner-radius of the cross-section $sec\;x$? Why isn't it $1 + sec\;x?$

• Because you're revolving about the line $y=1$. – paw88789 Sep 12 '14 at 1:45
• Will you please elaborate? – Jamie Kudla Sep 12 '14 at 1:45
• Did you do the sketching step? That may help. Also I am assuming you are only looking at one branch of the secant function, although that is not clear from the problem's statement. – paw88789 Sep 12 '14 at 1:49
• Yes,I have the correct graph in front of me. Every problem I've done up to now the inner-radius has just been the curve. You said it was because it's revolving around y=1, does that mean if it revolved around y=2 the inner-radius would be [(1 + secx) -2]? – Jamie Kudla Sep 12 '14 at 1:57

Its easy to see that the rectangle formed will have the width $\delta x$ and height $y+1 - 1 = (\sec x + 1)- 1 = \sec x$