After cutting a cone into two half cones, the sum of the surface areas of the two cones increases by 24 square centimeters compared to the original one. It is known that the height of the cone is 6 cm. What is the volume of the original cone?
把一个圆锥切成两个半圆锥后，两个圆锥的表面积的和比原来增加了24平方厘米，已知圆锥高6厘米，原来圆锥的体积是多少？
<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>