做一个无盖的圆柱形水桶，若要使体积是27π，且用料最省，则圆柱的底面半径为______．
设圆柱的高为h，半径为r
则由圆柱的体积公式可得，πr2h=27π
h=27 r2
S全面积=πr2+2πrh=πr2+2πr•
=πr2+27 r2 54π r
（法一）令S=f（r），（r＞0）
f′(r)=2πr-
=54π r2 2π(r3-27) r3
令f′（r）≥0可得r≥3，令f′（r）＜0可得0＜r＜3
∴f（r）在（0，3）单调递减，在[3，+∞）单调递增，则f（r）在r=3时取得最小值
（法二）：S全面积=πr2+2πrh=πr2+2πr•
=πr2+27 r2 54π r
=πr2+
+27π r
≥327π r
=27π3 πr2•
•27π r 27π r
当且仅当πr2=
即r=3时取等号27π r
当半径为3时，S最小即用料最省
故答案为：3
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| Some myths (神话) are stories told since ancient times to explain the causes for natural happenings. The Greek myth that explains why there are changes of 1 is about Demerter, the goddess of the harvest. She had a daughter, Persephone, whom she loved very much. Hades, god of the underworld, fell in love with Persephone, and he asked Zeus, the 2 of the gods, to give Persephone to him as his 3 . Zeus did not want either to disappoint Hades or to upset Demeter, so he said he would not agree to the marriage, but neither would he 4 it. Hades, therefore, decided to take the girl without 5 . When Persephone was picking flowers in the garden, he seized her and took her to the underworld. When Demeter 6 what happened to Persephone, she became so 7 that she caused all plants to 8 . People were in 9 of starving (挨饿). But Demeter was determined not to let crops grow 10 her daughter, Persephone, was returned to her. 11 , still not wanting to disappoint Hades, decided upon a condition for Persephone's 12 . She could go back to her mother if she had not 13 anything while she was in the underworld. Demeter 14 it because she did not know that Persephone had eaten several Pomegranate (石榴) seeds in the underworld. When Zeus 15 this, he agreed that Persephone could spend part of the year with her 16 , but he added that since she had eaten the seeds, she must spend part of the year in the underworld. And so it 17 that when Persephone is in the underworld, Demeter is sad and therefore 18 not let the crops grow. That is 19 we have winter when plants do not grow. When Persephone returns, Demeter is 20 , it is spring, and plants begin to grow again. | ||||
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