Cut a cone into parts of the same shape and size along the diameter and height of the bottom surface, if the sum of the surface area increases by 48 cm. Given that the height of the cone is 8 cm, what is the volume of the original cone in cubic centimeters?
把一个圆锥沿底面直径和高切成形状、大小完全一样的部分，如果表面积之和比原来增加了48厘米．已知圆锥的高为8厘米，原来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">48 / 2</gadget>
<output>24</output>

<gadget id="calculator">2 / 8</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">24 * (1/4)</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 * 8</gadget>
<output>75.36</output>

<result>75.36</result>