6 E - Related Rates WKST
Directions: Solve the following problems. Show all work clearly and neatly
1. As water pours into a cylindrical tank with radius 8 cm, the height of the water (h) in the tank increases at a rate of x cm per second. (V = ??r"h)
a. Find the rate that the radius, r, of the tank is changing, in cm per second, at any time t.
The radius is not changing; it is 0 cm/sec
it is fixed / constant at 8 cm.
b. Find the rate that the volume of the tank is changing, in cm3 per second, when x = 2 cm per second
rate of changing height
Find dv/dt | dh/dt = 2
V = ?r"h
dv/dt = ?r" (dh/dt)
dv/dt = ? " 8" " (2)
dv/dt = 128?
The rate the volume is changing is 128? cm3/sec when x=2 cm per second.
c. The rate that the height of water in the tank is increasing is a function of the height of water in the tank and can be modelled by the function x(h) = 4e3?? + 1. Find the rate that the volume of water in the tank is changing, in cm3 per second, when the tank contains 192? cm3 of water.
Find dv/dt | v = 192?
V = ? 8" h
V = 64? h
192? = 64? h / 64?
h = 3
X(3) = 4e3?3 + 1 = 5 height of water in tank
= 4(1) + 1 = 5
x'(h) = 4e3??(-dh/dt)
