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Question

Water is poured into a conical container at the rate of 10 cm3/sec. The cone points directly down, and it has a height of 25 cm and a base radius of 5 cm. How fast is the water level rising when the water is 4 cm deep (at its deepest point)?

Answer 1

Given: Volume=1/3(r^2)(pi)(h)

           dv/dt= 10

 

Let's set up a proportion from similar triangles:

 

r/h = 5/25  ---->  r=h/5

 

So Volume=(1/3)(h^3)(pi)(1/25)

               =(pi/75)(h^3)

 

Therefore, dv/dt=(pi/25)(h^2)(dh/dt)

 

Plugging givens in and height (h):

 

10=(16pi/25)(dh/dt)  ------->  dh/dt=250/(16pi)