<PRE><B>Question 736970</B>
 A circular cylinder is 60 inches in height and has a volume of 30 gallons.
 water is flowing into the cylinder at the rate of 5 gallons per minute.
 At what rate is the level of water in the cylinder increasing? 
:
30 gallons = 231*30 = 6930 cu/inches
:
Find the radius of the cylinder
pi*r^2*60 = 6930
{{{r^2}}} = {{{6930/(60*pi)}}}
{{{r^2}}} = 36.7648
r = {{{sqrt(36.7648)}}}
r ~ 6.1 inches
:
Find the height (h) of a cylinder of 5 gallons of water
5 * 231 = 1155 cu/inches
:
{{{pi*6.1^2*h}}} = 1155
h = {{{1155/(36.7648*pi)}}}
h = 9.99 ~ 10 inches per minutes</PRE>