A cone is cut into two equal parts along the diameter of the base, and the surface area is increased by 18cm**2. It is known that the height of the cone is 6cm. What is the volume of the cone in cm**3?
把一圆锥沿着底面直径切割成相同的两部分，结果表面积增加了18cm**2，已知圆锥的高是6cm，那么圆锥的体积是多少cm**3？
<gadget id="calculator">18 / 2</gadget>
<output>9</output>

<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>

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

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

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(3/2) ** 2</gadget>
<output>9/4 = around 2.25</output>

<gadget id="calculator">(1/3) * 3.14 * (9/4) * 6</gadget>
<output>14.13</output>

<result>14.13</result>