Water is pouring into a cylindrical bowl of height 10 ft. and radius 3 ft, at a rate of #5" ft"^3/"min"#. At what rate does the level of the water rise?

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Answer 1 · 2016-09-01T14:16:27

#= (5)/(9 pi )# ft/min

For a given height, #h#, of fluid in the cylinder or radius #r#, the volume is

#V = pi r^2 h#

Differentiating wrt time

#dot V = 2 pi r dot r h + pi r^2 dot h# but #dot r = 0# so

#dot V = pi r^2 dot h#

# dot h = dot V/( pi r^2) #

#= (5)/(pi (3^2))#

#= (5)/(9 pi )# ft/min