Question

Jesse has constructed a huge cylindrical can with a diameter of 60 ft. The can is being filled with water at a rate of 450 ft3/min. How fast is the depth of the water increasing? (Hint: The volume of water in the cylinder is determined by πr2h where r is the radius and h is the depth of the water )

Answer 1

450 ft^3/min=surface area

Answer 2

surface area=pir^2

Answer 3

this is a related rates question.

so you know the the radius is 30ft

then the volume is

\[V = \pi r^2h\]

so you need the derivative of the volume with respect to height.

or

\[\frac{dV}{dh}\]

then take the reciprocal to get \[\frac{dh}{dV}\]

and you know

\[\frac{dV}{dt} = 450 \]

then you need the chain rule

\[\frac{dh}{dt} = \frac{dh}{dV} \times \frac{dV}{dt}\]

you can plug the radius of 30 in at any time.

hope it helps

Answer 4

Was für ein Mensch bist du? Bist du Lehrer? Denn das ist so beeindruckend .