16. Sand is pouring out of a pipe and is forming a conical pile on the ground. 4
ID: 2846977 • Letter: 1
Question
16.Sand is pouring out of a pipe and is forming a conical pile on the ground.
4 meters per hour and the height is decreasing at a rate
of 1 meter per hour.
When the base is 10 meters and the height is 16 meters,
then how fast is the HYPOTENUSE changing?
The rate of change of the HYPOTENUSE is meters per hour.
(Enter your answer as a integer or as a decimal number rounded to 2 places.)
18.The length of a rectangle is increasing at a rate of
2 meters per hour and the width is increasing at a rate
of 1 meter per hour.
When the length is 13 meters and the width is 21 meters,
then how fast is the AREA changing?
The rate of change of AREA is square meters per hour.
(Enter your answer as an integer.)
19.At 3 PM a red car is 150 miles north of Bellevue
and a blue car is 170 miles east of Bellevue.
The red car drives north and the blue car drives west.
The red car is going 30 miles per hour and
the blue car is going 70 miles per hour.
The day is cloudy.
a) How far apart are the cars? miles
b) What is the rate of change of the distance between the cars? miles/hr
(Note: The locations and directions are important.)
(Enter each answer as decimal rounded to 2 places.)
20.An inverted pyramid is being filled with water at a constant rate of 40 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 8 cm, and the height is 15 cm.
Find the rate at which the water level is rising when the water level is 6 cm.
cm/sec
22.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 equal. How fast is the height of the pile increasing when the pile is 22 feet high?
Volume= 1/3 pi (radius)2 hegiht 1/4 93 7 6.5 28 2 V = 1/3 pi r2hExplanation / Answer
16)
V = 1/3*pi*r^2 *h
h = r/4
V = pi/12 * r^3 ......................(1)
dV = 3*pi/12 *r^2 *dr.............(2)
(2)/(1) will give
dV/V = 3*dr/r
When r=20 ;
V = pi/12 *20^3 = 2094.395 m^3
so
dV = V*dr/r = 2094.395*3/20 = 314.16 m^3/day
so answers :
a) 2094.395 m^3
b)314.16 m^3/day
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