Mathematics

Problem

A solid has base on the interval

0\le x\le3

. At each

x

the cross section perpendicular to the

x

-axis is an equilateral triangle whose side length is

k\sqrt{x}

, where

k>0

is a constant. If the volume of the solid is

\dfrac{9\sqrt{3}}{2}

cubic units, what is the value of

k

? a)

4

\sqrt{2}

2

2\sqrt{2}