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The document provides instructions for solving related rates problems involving a spherical balloon deflating. It identifies finding the rate air is removed when the radius is 9 cm as the problem. It sets up the equation relating volume, radius, and their rates of change and takes the derivative. Substituting the known radius and radius rate allows solving for the required air removal rate of -4860π cm3/min.
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- 1. Related Rates Harry Shontz Pd 6
- 2. Solving Related Rates Problems Identify what you are being asked to find and look for the given rate Create an equation relating the variables Take the derivative Substitute the known values and solve
- 3. Pg 224, Ex 15 A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min. At what rate must air be removed when the radius is 9 cm?
- 4. Identify What You Are Being Asked to Find and Look for the Given Rate Find dV/dt when the r = 9 dr/dt = -15 cm/min
- 5. 2. Create an Equation Relating the Variables V =(4/3)πr^3
- 6. 3. Take the Derivative V =(4/3)πr 3 dV/dt = 3(4/3)(πr 2 ) (dr/dt) dV/dt = 4πr 2 (dr/dt)
- 7. 4. Substitute the Known Values and Solve dV/dt = 4πr 2 (dr/dt) dV/dt = 4π(9) 2 (-15) dV/dt = -4860π
- 8. Therefore: Air must be removed from the balloon at a rate of 4860π cm 3 /min when the radius is 9 cm