Question

1. Lemonade is dripping from a conical filter with lemons in it, into a cylindrical pot at the rate of 12 in³ /min. How fast is the lemonade level in the cylindrical pot rising when the lemonade in the cone is 6in high? How fast is the height/level of the lemonade in the cone falling at that time?

2. A bird watcher is sitting in a stand that is 30ft. high and 15ft. to the left of a pole with a light. The light, which is at the top of the 30ft high pole, is facing the birdwatcher’s stand, but pointed toward the ground. The bird watcher accidentally drops his morning coffee from his 30ft. high stand. How fast is the shadow of the coffee cup moving along the ground 0.75 seconds later? Assume the coffee falls at a distance s=16t² in t seconds.

Answer 1

Soliction: a cone of readius en and We know the volume of a height h is : VE 13 ru²h cylinder of radius ir We know that the volume of height and h is : V = Tr²h the We know that, from the statement, the rate of change of both of volume of filter and the volume of cylindrical pot is : 12 in /min dv dt H 3. We can also see that the diameter and the height of the filter is 6, which means h=2r (for the core) The radius of cylinder is always # Lemonade level inthe cylindrical pot suicing when the lemonade in the cone is 6 in high. (inco h=6) dh The radius of find the pot is u=3. We have to V= Tr²h at T. 9.h = IT dh dt dv dt from , 1 dv dh dt 12 in/min. = 4 infrin IT It gr 3T

> dh dt 4 in/min 3 Auswer dh dt 4 in/min 2 3 T falling # Height / level of the lemonade in the come at that time : also The height of the full cone is h=6 in, which means that r = 3 in. We have to find dh It V= / Tu²h . (h) ² h I h JT 3 VE 12 . dr dv dt 12 3h² dh at 12 dh at dv dt JE 342 dh 4 dv T. (6) 2 at di The sign of the rate of change of volume 4. . dh dt (-12) 36T is negative because the volume is decreasing}. ch 4 3T in/min dt Auswer