Upper Radius
Nov 17
2009
2009
Comments Off
Related Rate Problem?
A paper cup containing water has the shape of a frustum of a right circular cone of altitute 6 inches, and lower and upper radius of 1 inch and 2 inches respectively. If water is leaking gout of the cup at a rate of 3 cubed inches per hour, at what rate is the water level decreasing when its depth is 4 inches?
if you could walk me through this i would really appreciate it.
thanks a bunch
The volume of the water in the cup at any moment is:
V = (1/3) pi [ (Rw)^2 + (1)Rw + (1)^2 ]
= (1/3) pi [ (Rw)^2 + Rw + 1 ] h
Rw = Radius of upper part of water
h = height of water
Rw / h = 2 / 6
6 Rw = 2 h
Rw = 1/3 h
Substitute in to the volume equation
V = (1/3) pi [ (1/9) h^2 + (1/3) h + 1] h
= (1/3) pi [ (1/9) h^3 + (1/3) h^2 + h ]
dV / dt = (1/3) pi [ (1/3) h^2 + (2/3) h + 1] (dh / dt)
Solve for dh /dt and plug in the values h=4 and dV/dt = 3
013- Radius – Dexterity (Upper Limb)
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