问题标题：
【Gravelisbeingdumpedfromaconveyorbeltatarateof10cubicfeetperminute.Itformsapileintheshapeofarightcircularconewhosebasediameterandheightarealwaysthesame.Howfastistheheightofthepileincreasingwhenthepileis】
问题描述：
Gravelisbeingdumpedfromaconveyorbeltatarateof10cubicfeetperminute.Itformsapileintheshapeofarightcircularconewhosebasediameterandheightarealwaysthesame.Howfastistheheightofthepileincreasingwhenthepileis24feethigh?
Recallthatthevolumeofarightcircularconewithheight"h"andradiusofthebase"r"isgivenbyV=(pir^2h)/3
宋庆君回答：
V=(pir^2h)/3题目说r始终和h相等,所以V=(pir^3)/3要求沙堆得高度变化h,由于传送带的速度是10cubicfeetperminute,所以dV=h^2pidh=10dtdh/dt=10/(h^2pi)因为h=24,带入得,dh/dt=0.0055此时高度的变化是0.0055feet...
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