Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. a. When using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. b. If a region is revolved about the y-axis, then the shell method must be used. c. If a region is revolved about the x-axis, then in principle, it is possible to use the disk>washer method and integrate with respect to x or the shell method and integrate with respect to y.

Calculus notes of 9/26/16 3.11 Related Rates Suppose a spherical weather balloon is filled with gas at a rate of 150 ft /min. What is the rate of change of its radius when the radius is 20 ft We are given / = 150: Volume increases by 150 ft /min. 3 dt dr We want / whedtr = 20 We need an equation relating V to r. 3 For a sphere, V = 4/3ᴨr dv 2 dr Different Rating time / = 4/3dt* 3r / (implicitdtifferentiation) 2 Or V’ = 4/3ᴨ * 3r r’ Solving for / , dt = dt(4ᴨr ) * /2 dvdt = 1/(4ᴨ * 20 ) * 150 = (3/32ᴨ) ft/min = 0.02984 ft/min Procedure: 1. Identify known rates and desired rates. Label what you alread