A 6 cm high cone wood block is divided into two pieces with the same shape and size along the diameter of the bottom surface, and the surface area increases by 24 square centimeters compared to the original one. What is the volume of this cone in cubic centimeters?
一块高6厘米的圆锥体木块，沿底面直径分成形状大小完全相同的两块后，表面积比原来增加了24平方厘米．这个圆锥体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">24 / 2</gadget>
<output>12</output>

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

<gadget id="calculator">12 * (1/3)</gadget>
<output>4</output>

<gadget id="calculator">4 / 2</gadget>
<output>2</output>

<gadget id="calculator">2 ** 2</gadget>
<output>4</output>

<gadget id="calculator">(1/3) * 3.14 * 4 * 6</gadget>
<output>25.12</output>

<result>25.12</result>