A conical tank is leaking water at the rate of 75 cubic inc/min. At the same time water is being pumped into the tank at a constant rate.The tanks height is 60 in whiles its top diameter is 20 inches.If the water level is rising at a rate of 5in/min when the height of the water is 10 inches high,find the rate in which water is being pumped into the tank to the nearest cubic inhes/min.The volume of a cone is given by( v= 1/3pi*r^2*h)

Question

amistre64 · Answer

A conical tank is 
   leaking water at the rate of 75 cubic inc/min. 

At the same time water is being pumped into the tank 
     at a constant rate.

The tanks height is 60 in 
        top diameter is 20 inches.

If the water level is "rising" at a rate of 5in/min 
       when the height of the water is 10 inches high

find the rate in which water is being pumped into the tank to the nearest cubic inhes/min.The volume of a cone is given by( v= 1/3pi*r^2*h)

thats easier to sort thru to me

amistre64 · Answer

Since the volume in the tank at any given time depends on how enters and exits it, we might be able to construct an equation to work with

amistre64 · Answer

we might as well start by deriving the given volume equation

V= 1/3pi*r^2*h

V' =2/3 pir h r' + 1/3 pir^2 h'

h' is the rate of rising = 5; h is given to be 10; so the radius at that moment is: h/r = 6, r = h/6; r = 10/6, 5/3

V' =10(2)(5)/3(3) pi r' + 5/3 pi (5/3)^2

amistre64 · Answer

since r = h/6 ; r' = h'/6; = 5/6

$$V' =\frac{10(2)(5)(5)}{3(3)(6)} pi + \frac{5\cdot 5^2}{3 \cdot 3^2} pi$$
$$V' =\frac{250}{27} pi + \frac{125}{27} pi$$
$$V' =\frac{375}{27} pi;\text{ at the given moment specfied}$$

amistre64 · Answer

we know the rate at which its leaving is: -75  so my hunch is to separate out the coming from the going to establish the rate of change that was determined from V'

$$V' = in' - out'=\frac{3(125)}{3(9)}pi $$

$$in' - 75=\frac{125}{9}pi $$
$$in'=\frac{125}{9}pi+75 $$

amistre64 · Answer

dunno how right it is, but thats how i would go about trying to solve it

anonymous · Answer

hey sorry im back i saw a few different ways but idk i first thought of doing some type of proportions?

anonymous · Answer

amistre that was dead on  just checked ur answer is one of the choices

amistre64 · Answer

cool :)