document.write( "Question 245091: A chemical is poured into a tank the shape of a cone with vertex down at the rate of 1/5 m^3/min (meters cuber per minute). if the radius of the cone is 6m and its height is 10 m, how fast is the liquid rising at the instant when the depth of the liquid is 2m in the center? \n" ); document.write( "

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A chemical is poured into a tank the shape of a cone with vertex down at the rate of 1/5 m^3/min (meters cuber per minute). if the radius of the cone is 6m and its height is 10 m, how fast is the liquid rising at the instant when the depth of the liquid is 2m in the center?
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\n" ); document.write( " $\"Vol+=+pi%2Ar%5E2%2Ah%2F3\"$
\n" ); document.write( "Eliminate r by solving for it in terms of h
\n" ); document.write( "r = 0.6h (that wasn't hard)
\n" ); document.write( " $\"V+=+pi%2A%280.6h%29%5E2%2Ah%2F3\"$
\n" ); document.write( " $\"V+=+pi%2A0.12h%5E3\"$
\n" ); document.write( "Differentiate wrt time
\n" ); document.write( "dV/dt = 3*pi*0.12h^2*dh/dt = 0.2
\n" ); document.write( "dh/dt = 0.2/(3*pi*0.12*4) at h=2
\n" ); document.write( "dh/dt =~ 0.0442097 meter/min
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