Cut a cylinder with a length of 72 cm into two small cylinders according to the ratio of 5:3. After cutting, the surface area increases by 12 square centimeters. What is the volume of the larger cylinder after cutting?
把长72厘米的圆柱体，按5：3截成两个小圆柱体，截开后表面积比原来增加了12平方厘米，求截开后较大的圆柱体的体积是多少立方厘米？
<gadget id="calculator">12 / 2</gadget>
<output>6</output>

<gadget id="calculator">5 + 3</gadget>
<output>8</output>

<gadget id="calculator">72 / 8</gadget>
<output>9</output>

<gadget id="calculator">9 * 5</gadget>
<output>45</output>

<gadget id="calculator">6 * 45</gadget>
<output>270</output>

<result>270</result>