Answer
$\dfrac{15 \pi}{32}$
Work Step by Step
Since, the vertical slices solid are circular discs , so we will use the disk method to compute the volume of revolution of the curve.
The volume of revolution of the curve can be expressed as: $V=\pi \int_p^q [f(x)]^2 dx\\=\pi \int_0^{\ln 4} (e^{-x})^2 \ dx \\= \pi \int_0^{\ln 4} e^{-2x} \ dx \\=\pi [\dfrac{-e^{-2x}}{2}]_0^{\ln 4} \\=\dfrac{\pi}{2} (1-e^{\ln 4^{-2}}) \\=\dfrac{15 \pi}{32}$
