If a cone-shaped wooden block with a base radius of 3 cm is cut into two parts of equal size along the height, the surface area is increased by 24 square centimeters, what is the volume of the cone in cubic centimeters?
把一个底面半径是3厘米的圆锥形木块沿高切成大小相等的两部分，表面积增加了24平方厘米，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">3 ** 2</gadget>
<output>9</output>

<gadget id="calculator">24 / 2</gadget>
<output>12</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</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">(1/3) * 3.14 * 9 * 4</gadget>
<output>37.68</output>

<result>37.68</result>