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

Answer 1

1. V = (1/3)*π*r²*h
2. h = 0.5*r so V = (1/3)*π*r²*(0.5*r) = (1/6)*π*r³
3. 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
4. Solve using simple algebra for dr/dt = (-70/400)*2/π = -0.111465 m/hr