Answer :
Water is increasing at a rate of ( 3/200π ) inch/min in a cylindrical tank.
As per the question we are provided with ,
r = 20 inch equation 1
( dV/dt ) = 6 cubic inch per min equation 2
We need to calculate (dh/dt) and to calculate this we can use the formula of volume of cylinder.
volume of cylinder = V
V = π[tex]r^{2} h[/tex] equation 3
Substitute value of r from equation 1 in equation 3, we will get
V = π × [tex](20^{2} )[/tex] × h
V = π (400) h
Differentiate with respect to time , we get
( dV/dt ) = 400π ( dh/dt )
Substitute value of ( dV/dt ) from equation 2 , we get
6 = 400 π ( dh/dt )
( dh/dt ) = ( 3/200π ) inch/min
Thus, ( 3/200π ) inch/min is the rate of increase of height of water.
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