APFIVE Volume with Equilateral Triangle Cross Sections
The base of a solid is the region enclosed by the graph of $$y = \ln(x)$$, the $$x$$-axis, and the lines $$x = 1$$ and $$x = e$$. If the cross sections of the solid perpendicular to the $$x$$-axis are equilateral triangles, what is the volume of the solid?
A
$$\displaystyle \frac{\sqrt{3}e}{4}$$
B
$$\displaystyle \frac{\sqrt{3}(e-2)}{4}$$
C
$$\displaystyle \frac{\sqrt{3}}{4}$$
D
$$\displaystyle \frac{\sqrt{3}(e-1)}{4}$$
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