For a cuboid block, the sum of the lengths of all its edges is 108 cm, and the ratio of its length, width, and height is 4:3:2. Now it is necessary to cut this cuboid into a cylinder with the largest volume. What is the volume of this cylinder in cubic centimeters?
一个长方体的木块，它的所有棱长之和为108厘米，它的长、宽、高之比为4：3：2．现在要将这个长方体削成一个体积最大的圆柱体，这个圆柱体体积是多少立方厘米？
<gadget id="calculator">108 / 4</gadget>
<output>27</output>

<gadget id="calculator">4 + 3 + 2</gadget>
<output>9</output>

<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">27 * (1/3)</gadget>
<output>9</output>

<gadget id="calculator">9 / 2</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">(9/2) ** 2</gadget>
<output>81/4 = around 20.25</output>

<gadget id="calculator">2 / 9</gadget>
<output>2/9 = around 0.222222</output>

<gadget id="calculator">3.14 * (81/4) * 27 * (2/9)</gadget>
<output>381.51</output>

<result>381.51</result>