CALC Derivatives - Related Rates

For each problem your work must include the equation used, its derivative and how it is used to solve a problem. Answers can be rounded to thousandths or as exact values. ALL CALCULUS WORK IS EXPECTED TO BE SHOWN CLEARLY FOR CREDIT. Include Units. 1. Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following rates: dx/dt = 1m/s, dy/dt = -2m/s, and dz/dt = 0.5m/s. At the instant x -4m, y =3m, and 2 = 5 m find the rates the following change: (a) volume of the box (b) surface area of the box (c) diagonal of the box [d = (x2 + yz + zz. ] 2. A spherical iron ball is coated with a layer of ice of uniform thickness. If the ice melts at the rate of 4 mL/min, how fast is the outer surface area of ice changing when the outer diameter of the ball with ice on it is 24 cm? (Hint: Need to work with both volume and surface area. Keep answers in terms of pi until the end - rounding isn't a good habit.) Convert the Units: 8 ml/min = 8 cm /min = dV/dt (6mL/min is a liquid rate of change which is a volume rate of change.)