A cone is cut from the apex along the height. Its surface area is increased by 60 square centimeters compared to the original one. The cross section is an equilateral triangle with a height of 6 cm. What is the volume of this cone?
一个圆锥从顶点沿高切开，其表面积比原来增加了60平方厘米，截面是一个高是6厘米的等边三角形，这个圆锥的体积是多少？
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">60 / 2</gadget>
<output>30</output>

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

<gadget id="calculator">30 * (1/3)</gadget>
<output>10</output>

<gadget id="calculator">10 / 2</gadget>
<output>5</output>

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>

<gadget id="calculator">(1/3) * 3.14 * 25 * 6</gadget>
<output>157</output>

<result>157</result>