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
1 Expert Answer
- V = (1/3)*π*r2*h
- h = 0.5*r so V = (1/3)*π*r2*(0.5*r) = (1/6)*π*r3
- dV/dt = (dV/dr)*(dr/dt).... dV/dr = 0.5*π*r2 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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