1. Let z = x^{2} + y^{2}, where x and y are increasing at the constant rates of 2 units per second and 3 units per second, respectively. What is the set of points for which the rate of change of z is zero?
A. {(x,y): 3y = 2x} 
B. {(x,y): 3y = 2x} 
C. {(x,y): x = y = 0} 
D. {(x,y): 2y = 3x} 
E. {(x,y): 2y = 3x} 

2. A water tank in the shape of a right circular cone has a height of 10 feet. The top rim of the tank is a circle with a radius of 4 feet. If water is being pumped into the tank at the rate of 2 cubic feet per minute, what is the rate of change of the water depth, in feet per minute, when the depth is 5 feet?
(The volume V of a right circular cone is V = 1/3 p r^{2}h, where r is its radius and h is its height.)
A. 1/2p 
B. 1/p 
C. 3/2p 
D. 2/p 
E. 5/2p 

3. A cube of ice melts without changing shape at the uniform rate of 4 cm^{3}/min. What is the rate of change of the surface area of the cube, in cm^{2}/min, when the volume of the cube is 125 cm^{3}?
A. 4 
B. û16/5 
C. û16/6 
D. 60/19 
E. 16/5 

4. Let x be the length of one of the equal sides of an isosceles triangle, and let q be the angle between them. If x is increasing at the rate 1/12 m/hr, and q is increasing at the rate of p /180 radians/hr, then at what rate, in m^{2}/hr, is the area of the triangle increasing when x = 12 m and q = p /4?
A. 36(2^{1/2}) 
B. (73/2)(2^{1/2}) 
C. (3^{1/2}/2)+(p /5) 
D. 2^{1/2}((1/2)+(1/5)p ) 
E. 2^{1/2}(6+(1/5)p ) 

5. The radius of a right circular cylinder increases at the rate of 0.1 cm/min, and the height decreases at the rate of 0.2 cm/min. What is the rate of change of the volume of the cylinder, in cm^{3}/min, when the radius is 2 cm and the height is 3 cm? (Note: The volume of a right circular cylinder is V = p r^{2}h.)
A. 2p 
B. 8p /5 
C. 3p /5 
D. 2p /5 
E. 2p 

6. The height h of a right circular cone is 20 cm and is decreasing at the rate of 4 cm/sec. At the same time, the radius r is 10 cm and is increasing at the rate of 2 cm/sec. What is the rate of change of the volume in cm^{3}/sec? (Note: The volume of a right circular cone is V = 1/3p r^{2}h.)
A. 400p 
B. 400p /3 
C. 0 
D. 400p/3 
E. 400p 
