Question

Water is flowing into a large spherical tank at a constant rate. Let V(t) be the volume of water in the tank and H(t) be the height of the water level at time t.
a) Give a physical interpretation of dV/dt and dH/dt.
b) Is dV/dt positive, negative, or zero when the tank is one-fourth full? Justify your answer.
c) Is dH/dt positive, negative, or zero when the tank is one-fourth full? Justify your answer.

Answer 1

Answer:

A) dV/dt = the rate of change of the given volume of water in the tank with respect to the time, t.

dH/dt = the rate of change of the height of the water in the tank with respect to the time

B) dV/dt is positive

C) dH/dt is positive

Step-by-step explanation:

We are given that;

V(t) is the volume of water in the tank and H(t) is the height of the water level at time t. Thus;

A) dV/dt = the rate of change of the given volume of water in the tank with respect to the time, t.

dH/dt = the rate of change of the height of the water in the tank with respect to the time

B) When the tank is one-fourth full, dV/dt is positive because the volume water in the tank is increasing with time.

C) when the tank is one-fourth full, dH/dt is positive because the height has increased from zero level to 0.25 times the height of the tank. Thus the height is increasing with time.