A solid has base on

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

A solid has base on

0\le x\le L

. At each

x

the cross section perpendicular to the

x

-axis is an equilateral triangle whose side length is

e^{-x/2}

. If the volume of the solid is

\dfrac{\sqrt{3}}{8}

cubic units, what is the value of

L

? (a)

\ln\left(\dfrac{3}{2}\right)

(b)

\dfrac{1}{2}

(c)

\ln 2

(d)

\ln\left(\dfrac{4}{3}\right)