13 The graphs of the functions $y=|x|$ and $y=\frac{6-x}{5}$ form a triangle $A O B$. When this triangle is rotated $\frac{2}{3}$ radians about the $x$-axis, the volume of the resulting solid is
A. $\frac{5}{6} \pi$
B. $\frac{5}{6}$
C. $\frac{5 \pi}{3}$
D. $\frac{5}{3}$
13 B. The two images intersect at $A\left(-\frac{3}{2}, \frac{3}{2}\right)$ and $B(1,1)$, the line segment $AB$ intersects the $y$-axis at $M\left(0, \frac{6}{5}\right)$, so the required volume is
$$
V=\left(V_{\text {frustum } A B}-V_{\text {cone } A M}-V_{\text {cone } M B}\right) \cdot \frac{1}{2 \pi} \cdot \frac{2}{3}=\frac{5}{6} .
$$