CPM Homework Help : CALC Problem 8-109

Given that a typical cross-section of a solid taken perpendicular to the x-axis has an area of $A(x) =\operatorname{ln} x$ , set-up an integral to calculate the volume of this solid from [ $a, b$ ]. Does it matter what the shape of the solid is? Explain.

Hint:

Of course every shape has a different area function, and this area function $=\operatorname{ln}x$ .
It is not possible to know what the cross-sections looks like. Perhaps they are rectangles with height $=\operatorname{ln}x$ and base $= 1$ ? But they could also be strange looking shapes. Just as long as all of their areas $=$ (coefficient)(base)(height) $=\operatorname{ln}x$ , the Volume by Cross Section formula will work.