Posted by andrew on Saturday, April 2, 2011 at 4:09pm.
6. A parabaloid with height h and radius r has volume 1/2 pieR^2H. Consider a parabaloidshaped water
tank with height of 7m and radius of 4m. If V is the volme of water in the tank and h is the depth
of water,
find the relationship between dV/dt and dhdt.
How is the volume changing when h = 3m and
dh/dt = 0.2m/s?

calculus  Damon, Saturday, April 2, 2011 at 5:06pm
dV/dt = surface area * dh/dt (geometry , no calculus really required, draw picture)
dV/dt = pi r^2 dh/dt

calculus  Reiny, Saturday, April 2, 2011 at 5:08pm
consider a crosssection of the paraboloid placed with vertex at the origin an opening upwards
then its equation would be
y = ax^2
when x=4, y = 7
y = (7/16)x^2
or
h = (7/16)r^2 , using r and h
r^2 = 16h/7
V = (1/2)πr^2h
= (1/2)π(16h/7)h
= (8π/7) h^2
dV/dt = 16π/7 h dh/dt > the relationship between dV/dt and dh/dt
Whe h=3 and dh/dt = .2
dV/dt = (16π/7)(3)(.2) = ......
I will let you do the button pushing.
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