### Home > CALC > Chapter 8 > Lesson 8.3.2 > Problem8-109

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.

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.