Consider a wedding cake of infinite height, each layer of which is a right circular cylinder of height 1.  The bottom layer of the cake has a radius of 1, the second layer has a radius of 1/2, the third layer has a radius of 1/3, and the nth layer has a radius of 1/n.    a.  Write the volume of the cake as an infinite sum in expanded form and in sigma notation. b.  Determine whether the volume converges or diverges by using the proper test c.  Do some research to find the exact volume of the cake

A concrete reservoir in the shape of a triangular prism is being filled with water at the constant rate of 2 cubic feet per minute. The reservoir is 4 feet deep, measures 6 feet across the top, and is 20 feet long (see figure). For any time t>=0, let H represent the depth of the water in the reservoir and let W represent the width of the rectangular region of water at the top. a. If the reservoir is initially empty, how long will it take to fill completely? b. How fast is the depth of the water in the reservoir changing when the reservoir is half-full? Remember to includes units. c. How fast is the rectangular area of the surface of the water changing when the reservoir is half full? Indicate units of measure.