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The volume of a right circular cylinder is given by V= πr2h, where r is the...

  1. The volume of a right circular cylinder is given by V= πr2h, where r is the radius of its circular base and h is its height.

  1. Differentiate the volume formula with respect to t to determine an equation relating the rates of change dV/dt , dr/dt , dh/dt.  
  1. At a certain instant, the height is 6 inches and increasing at 1 in/sec and the radius is 10 inches and decreasing at 1 in/sec. How fast is the volume changing at that instant? Is the volume increasing or decreasing? How can you tell?
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