WeBWorK : Winter-2017 LTX webwork latech.edu/webwork2/Winter201718-Math241-Crow/

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WeBWorK : Winter-2017 LTX webwork latech.edu/webwork2/Winter201718-Math241-Crow/stewartBe_ch03509/2/user-ecb0238efectiveUser-ecb023&key-Fldgiz4IWI; ourses Homework Sets stewart8e ch03s09: Problem 2 stewart8e ch03s09 Problem 2 Previous Problem Problem List Next Problem User Settings (1 point) Gravel is being dumped from a conveyor belt at a rate of 50 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 23 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by Grades Problems Problem 1 .. Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Rate- view My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining Email instructor 5:31 PM lype here to search 1/23/2018 47

Explanation / Answer

V=(1/3) pi r2h

h=2r

r=h/2

V=(1/3) pi(h2/4)h =(1/12)pi h3

dV/dt=(3/12) pi h2(dh/dt) =(1/4) pi(23)2(dh/dt)

50=(1/4) pi 529(dh/dt)

dh/dt=50*4/(pi *529)=0.12 ft/minute

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