Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute.It forms a pile in the shape of a right circular cone whose base diameter and height are always the same.How fast is the height of the pile increasing when the pile is 24 feet high?Recall that the volume of a right circular cone with height "h" and radius of the base "r" is given by V=(pi r^2h)/3
问题描述：
Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute.It forms a pile in the shape of a right circular cone whose base diameter and height are always the same.How fast is the height of the pile increasing when the pile is 24 feet high?
Recall that the volume of a right circular cone with height "h" and radius of the base "r" is given by V=(pi r^2h)/3
答
V=(pi r^2h)/3题目说r始终和h相等,所以V=(pi r^3)/3要求沙堆得高度变化h,由于传送带的速度是10cubic feet per minute,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0.0055 feet...