Answer:
the rate of increase of radius is dR/dt = 0.804 m/hour = 80.4 cm/hour
Explanation:
the slick of oil can be modelled as a cylinder of radius R and thickness h, therefore the volume V is
V = πR² * h
thus
h = V / (πR²)
Considering that the volume of the slick remains constant, the rate of change of radius will be
dh/dt = V d[1/(πR²)]/dt
dh/dt = (V/π) (-2)/R³ *dR/dt
therefore
dR/dt = (-dh/dt)* (R³/2) * (π/V)
where dR/dt = rate of increase of the radius , (-dh/dt)= rate of decrease of thickness
when the radius is R=8 m , dR/dt is
dR/dt = (-dh/dt)* (R³/2) * (π/V) = 0.1 cm/hour *(8m)³/2 * π/1m³ *(1m/100 cm)= 0.804 m/hour = 80.4 cm/hour
Answer:
The volume up to cylindrical portion is approx 32355 liters.
Explanation:
The tank is shown in the attached figure below
The volume of the whole tank is is sum of the following volumes
1) Hemisphere top
Volume of hemispherical top of radius 'r' is

2) Cylindrical Middle section
Volume of cylindrical middle portion of radius 'r' and height 'h'

3) Conical bottom
Volume of conical bottom of radius'r' and angle
is

Applying the given values we obtain the volume of the container up to cylinder is
Hence the capacity in liters is 
Answer:
The answer is "Option B".
Explanation:
Given equation:

if

Calculating by the Routh's Hurwitz table:

Form the above table:

In the above, the value of k is greater than 1.