The original plan was to use iron sheets to make a cylindrical bucket without a cover, with a height of 50 cm. Because according to needs, the height of the bucket actually made increases by 10 centimeters, and the side area increases by 628 square centimeters. How many square centimeters of iron sheets are needed to make this bucket?
原计划用铁皮制一个无盖的圆柱形水桶，高是50厘米．因根据需要，实际做的水桶的高增加了10厘米，则侧面积增加了628平方厘米，做这个水桶至少需要多少平方厘米的铁皮？
<gadget id="calculator">628 / 10 / 3.14 / 2</gadget>
<output>10</output>

<gadget id="calculator">10 ** 2</gadget>
<output>100</output>

<gadget id="calculator">3.14 * 100</gadget>
<output>314</output>

<gadget id="calculator">628 / 10</gadget>
<output>314/5 = around 62.8</output>

<gadget id="calculator">50 + 10</gadget>
<output>60</output>

<gadget id="calculator">(314/5) * 60</gadget>
<output>3_768</output>

<gadget id="calculator">314 + 3_768</gadget>
<output>4_082</output>

<result>4_082</result>