Respuesta :
The rate of rising water level can be calculated by the differentiation of volume formula. The rate of rising water level is 0.48 m/min.
The shape of a water tank is a circular cone, so the volume can be calculated by:
[tex]V = \dfrac {\pi r^2 h}3[/tex]
Where,
[tex]V[/tex] = volume,
[tex]r[/tex] = base radius,
[tex]h[/tex] = height or water level
To calculate the rate differentiate both sides with respect to time. Assume radius [tex]r[/tex] as constant.
[tex]\dfrac {dV}{dt} = \pi r^2(\dfrac {dh}{dt})\dfrac 13[/tex]
Given here,
[tex]\dfrac {dV}{dt} = 2m^3/min\\\\r = 2m[/tex]
Put the values in the formula,
[tex]\ \ \ 2 = \pi 2^2\times {\dfrac {dh}{dt }\times \dfrac 13}\\\\\dfrac {dh}{dt} = 0.48\rm \ m/min[/tex]
Therefore, the rate at which of rising water level is 0.48 m/min.
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