Cut a cone into two parts with the same shape and size along the diameter and height of the bottom surface. The result is that the sum of the surface area increases by 48 square decimeters compared to the original one. The height of the cone is known to be 6 decimeters. What is the volume of the original cone? cubic decimeter?
把一个圆锥沿底面直径和高切成形状、大小完全一样的两部分，结果表面积之和比原来增加了48平方分米，已知圆锥的高为6分米，求原来圆锥体的体积是多少立方分米？
<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 / 6</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">24 * (1/3)</gadget>
<output>8</output>

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

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>

<gadget id="calculator">(1/3) * 3.14 * 16 * 6</gadget>
<output>100.48</output>

<result>100.48</result>