Worksheet 3.8 Related Rates - Calculus Maximus Page 5
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7Calculus Maximus
WS 3.8: Related Rates
8. (2002 AB5) A container has the shape of an open right circular
cone, as shown in the figure below. The height of the container is
10 cm and the diameter of the opening is 10 cm. Water in the
container is evaporating so that its depth h is changing at the
3
constant rate of
cm/hr.
10
h
(a) Find the volume V of water in the container when
cm.
5
Indicate units of measure.
h
(b) Find the rate of change of the volume of water in the container, with respect to time, when
5
cm.
Indicate units of measure.
(c) 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?
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