Chapter 5 - Applications Of The Definite Integral In Geometry, Science, And Engineering - 5.2 Volumes By Slicing; Disks And Washers - Exercises Set 5.2 - Page 363: 26

\begin{align} b = \frac{2\pi}{6+\pi} \end{align}

$\text{It is given that}$ \begin{align} y \frac{1}{x}; y = 0; x =2 \ and \ x = b \ (0 \leq b \leq 2) \end{align} $\text{We have to find b, so that the volume of the solid is 3. Therefore:}$ \begin{align} V = \int_b^2 \pi \frac{1}{x^2} \ dx = \pi \times \left[-\frac{1}{x} \right]_b^2 = \pi \times \left(\frac{1}{b} - \frac{1}{2} \right) = 3 \Rrightarrow b = \frac{2\pi}{6+\pi} \end{align}