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How to go about this related rates question?
Wheat falls from an overhead bin and accumulates in a conical pile, so that the radius of the base of the cone is always twice the height of the cone. If the wheat falls at a rate of 3 m3/min, how fast is the height of the wheat pile changing when the diameter of the pile is 20 meters
2 Answers
- 6 years ago
Draw a picture. V=(1/3)pi r^2h, and you want dh/dt when r=10 meters. But r=2h, so V=(1/3)pi(2h)^2*h=[(4pi)/3]h^3. Apply d/dt to both sides and get (using the chain rule, so dh^n/dt=dh^n/dh*dh/dt=nh^{n-1}dh/dt)
dV/dt=4pi h^2 dh/dt. You know dV/dt=3. You only need h at that moment when diameter=20, so radius=10, so h=r/2=5. I'll let you finish (and check my work).
- ted sLv 76 years ago
V = [ 1 / 3 ] π r² h , given dV / dt =3 [ cu m ] and r = h / 2....find dh / dt when h = 20...do the computations