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9 Nov 2019
Rates of Change: please show work
A gravel plant crushes gravel into sand. The sand falls from a spout and forms a right circular cone whose radius is always twice its height. The radius of the base is increasing at the rate of 6 inches per minute. The volume of a cone with radius r and height h is given by V = 1/3 pir2h. Find the rates in which the circumference of the base and the area of the base are changing when the radius is 8 inches. Specify units. Find the rate at which the volume of the sand cone is changing when its height is 5 feet. Specify units. When the height of the sand cone reaches 5 feet, the rate at which its volume changes remains constant. A suction device then switches on, takes the sand away and puts it on train cars. The rate at which the sand is suctioned off the cone is given by .Find the time t in minutes since the suction device started when the volume of the sand pile is not changing.
Rates of Change: please show work
A gravel plant crushes gravel into sand. The sand falls from a spout and forms a right circular cone whose radius is always twice its height. The radius of the base is increasing at the rate of 6 inches per minute. The volume of a cone with radius r and height h is given by V = 1/3 pir2h. Find the rates in which the circumference of the base and the area of the base are changing when the radius is 8 inches. Specify units. Find the rate at which the volume of the sand cone is changing when its height is 5 feet. Specify units. When the height of the sand cone reaches 5 feet, the rate at which its volume changes remains constant. A suction device then switches on, takes the sand away and puts it on train cars. The rate at which the sand is suctioned off the cone is given by .Find the time t in minutes since the suction device started when the volume of the sand pile is not changing.