A cone with a height of 12 cm is cut vertically along the height into two half cones, the sum of the surface areas increases by 72 cm2 compared to the original one, find the volume of the original cone.
把一个高为12cm的圆锥沿高竖直切开成两个半圆锥，表面积之和比原来增加了72平方厘米，求原来圆锥的体积．
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">72 / 2</gadget>
<output>36</output>

<gadget id="calculator">2 / 12</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">36 * (1/6)</gadget>
<output>6</output>

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

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

<gadget id="calculator">(1/3) * 3.14 * 9 * 12</gadget>
<output>113.04</output>

<result>113.04</result>