### Home > APCALC > Chapter 8 > Lesson 8.3.2 > Problem8-110

8-110.

Given that a typical cross-section of a solid taken perpendicular to the x-axis has an area of $A(x) = \ln(x)$, 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. Homework Help ✎

$\text{volume by cross-sections }= \int_{a}^{b}(\text{area})dx$

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