Divide a cone into two parts with equal volume and same shape along the diameter of the bottom surface. The surface area is increased by 120 square centimeters compared to the original one. The height of the cone is 6 cm. What is the volume of the cone in cubic centimeters?
把一个圆锥沿底面直径分成体积相等、形状相同的两部分，表面积比原来增加了120平方厘米，圆锥的高为6厘米，圆锥的体积是多少立方厘米？
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">120 / 2</gadget>
<output>60</output>

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

<gadget id="calculator">60 * (1/3)</gadget>
<output>20</output>

<gadget id="calculator">20 / 2</gadget>
<output>10</output>

<gadget id="calculator">10 ** 2</gadget>
<output>100</output>

<gadget id="calculator">(1/3) * 3.14 * 100 * 6</gadget>
<output>628</output>

<result>628</result>