Expert: Abe Mantell - 6/6/2009

Question
1.Gravel is being dumped from a conveyor belt at a rate of 40 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 20 feet high? Recall that the volume of a right circular cone with height h and radius of the base r is given by V= 1/3pir^2h.

2.A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 11 km and climbs at an angle of 20 degrees. At what rate, in km/min is the distance from the plane to the radar station increasing 2 minutes later?

could you run me thru the steps with the answer. i'm so confused on these types of related rate problems.

Answer
Hello Brooke,

1. We differentiate V=(1/3)pi*r^2*h with respect to "t" but first let
.  r=h/2 (since h=diameter), so V=(1/3)pi*(h/2)^2*h=(1/12)pi*h^3
.  Thus, V'=(3/12)pi*h^2*h'...now let V'=40 and h=20 and solve for h'
.  40=(1/4)pi*400*h' ==>40=100pi*h' ==> h'=40/(100pi) ft/min

2. Didn't I answer this one for you just recently???

TTYL, Abe