Homework Help: calculus

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 parabaloid-shaped 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 cross-section 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.

Answer this Question

Related Questions

Calculus I - *Optimization problem* [I don't know how to get to the answer] ...
Math - Calculus 2 - An underground tank full of water has the following shape: ...
Calculus - Water is draining at a rate of 2 cubic feet per minute from the ...
Calculus - The volume of a cone of radius r and height h is given by V=1/3pir^2h...
Calculus - A water tank is shaped like an inverted right circular cone with a ...
Calculus - The volume of a cone of radius r and height h is given by V=(1/3)pir^...
Calculus HARD NEED HELP - The volume of a cone of radius r and height h is given...
math - Suppose we pump water into an inverted right-circular cone tank at the ...
Algebra!! - 1.a swimming pool has a radius of 10 feet and a height of 4 feet. ...
Calculus - The radius of a tank can not exceed 5m, and the height can not exceed...

For Further Reading

First Name:
School Subject:
Answer: