Question 1187852
<pre>
{{{drawing(275,400,-6,5,-1,15,

line(-5,0,-5,12), locate(-5.8,6,60),line(-5.5,0,-4.5,0),line(-5.5,12,-4.5,12),
line(0,0,-4,12),line(0,0,4,12), line(0,12,4,12), line(0,0,0,12), line(0,6,2,6),
arc(0,12,8,-4), arc(0,6,4,-2), locate(-.5,3.8,x), locate(1,6.59,r),locate(2,12.6,20)
 )}}}

Because of similar right triangles,

{{{r/x}}}{{{""=""}}}{{{20/60}}}
{{{r/x}}}{{{""=""}}}{{{1/3}}}
{{{3r}}}{{{""-""}}}{{{x}}}
{{{r}}}{{{""=""}}}{{{expr(1/3)x}}}

The formula for the volume of a cone is 

{{{V}}}{{{""=""}}}{{{expr(1/3)(pi*r^2h)}}}

Substituting {{{h=x}}} and {{{r=1/3}}},

{{{V}}}{{{""=""}}}{{{expr(1/3)(pi*(expr(1/3)x)^2(x))}}}
{{{V}}}{{{""=""}}}{{{expr(1/3)(pi*expr(1/9)x^3)}}}
{{{V}}}{{{""=""}}}{{{pi*x^3/27^"")}}}{{{cm^3}}}
</pre>ii) find the rate of increase of x at the instant when x=2.<pre>


{{{dV/dt}}}{{{""=""}}}{{{expr(pi/27)3x^2*expr(dx/dt)}}}
{{{dV/dt}}}{{{""=""}}}{{{((pi*x^2)/9^"")expr(dx/dt)}}}
{{{40}}}{{{""=""}}}{{{((pi*2^2)/9^"")expr(dx/dt)}}}
{{{40}}}{{{""=""}}}{{{(4pi/9)expr(dx/dt)}}}

Divide both sides by 4

{{{10}}}{{{""=""}}}{{{(pi/9)expr(dx/dt)}}}

Multiply both sides by {{{9/pi}}}

{{{90/pi}}}{{{""=""}}}{{{dx/dt}}}

Answer: The water level is rising at the rate of 90/&pi; or about 28.6 centimeters per second.

Edwin</pre>