Assignment:
A container has the shape of an open right circular cone. The height of the container is 10cm and the diameter of the opening is 10cm. Water in the container is evaporating so that its depth h is changing at the constant rate of -3/10 cm/hr.
Show that the rate of change of the volume of water in the container due to evaporation is directly proportional to the exposed surface area of the water. What is the constant of proportionality?
(Note: The volume of a cone of height h and radius r is given by V = 1/3(pi*r^2*h)
Provide complete and step by step solution for the question and show calculations and use formulas.