Sand is pouring out At 70 m3 per hour and is forming a conical pile on the ground the height is always 1/2 of the radius when the pile has a radius of 20 m the radius is increasing at a rate of

Arman G.
answered • 11/14/19

Aerospace Engineer

V = (1/3)*π*r^{2} *h
h = 0.5*r so V = (1/3)*π*r^{2} *(0.5*r) = (1/6)*π*r^{3}
dV/dt = (dV/dr)*(dr/dt).... dV/dr = 0.5*π*r^{2} and we're solving for dr/dt so dV/dt = 0.5*π*(20) ^{2} *(dr/dt) = -70
Solve using simple algebra for dr/dt = (-70/400)*2/π = -0.111465 m/hr
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