Question

Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a constant rate of 5 cubic feet per minute. If the pool has radius 7 feet and height 9 feet, what is the rate of change of the height of the water in the pool when the depth of the water in the pool is 7 feet?

Answer 1

this is what i tried. dint work

Answer 2

I can suggest something if you want.

Answer 3

sure!

Answer 4

Something between your work and question don't match up.....

Answer 5

Is this supposed to be 2 questions?

Answer 6

oh shoot

Answer 7

never mind thanta for a totally different question

Answer 8

thnx for pointing out

Answer 9

But, do you need help for the first question?

Answer 10

yes

Answer 11

V is a funtion of t

V(t) = 5t

now think of h as a funtion of t h(t)

h(t) = ((pi) r^2)/V(t)

=> h(t) = (pir^2)/5t

set h(t) = 7, find t

differentiate h(t) and plug in t

Answer 12

V = pi * r^2 * h

Answer 13

V = pi * 7^2 * h

Answer 14

V = pi * 49h

Answer 15

dV/dh = 49pi

Answer 16

dV/dt * dt/dh = 49pi

Answer 17

5 * dt/dh = 49pi

Answer 18

dt/dh = 49pi/5

Answer 19

dh/dt = 5/(49pi) =

Answer 20

I might have made a mistake somewhere, correct
me if I did.

Answer 21

=.32057
ill check

Answer 22

will the units be ft/min?

Answer 23

yes

Answer 24

its incorrect

Answer 25

Ya, I just noticed I made a mistake

Answer 26

one sec.

Answer 27

@zordoloom did you realize your mistake?

Answer 28

Ya, The h wasn't calculated properly.

Answer 29

you mean 7^2 pi?

Answer 30

That part, yes

Answer 31

@zordoloom do you know what it should be?

Answer 32

=.017897 ill check if its right

Answer 33

incorrect

Answer 34

h' was supposed to be the final answer right?

Answer 35

wait

Answer 36

it;s (5*27)/(49^2 pi) right?

Answer 37

i'm taking a screen shot. u tell me if i put it in correct. wait

Answer 38

did you get it?

Answer 39

i'll try that wait

Answer 40

did u get it? its incorrect

Answer 41

i guess. thankyou very much for trying

Answer 42

would the units be feet/min for sure? maybe thats whats wrong

Answer 43

yeah i know. rounding to decimals for sure

Answer 44

V=Ah
then dh/dt=dv/dt/A
dh/dt=5/7^2pi

Answer 45

let me try it

Answer 46

=.3205706789
did not work

Answer 47

0.032057

Answer 48

not correct

Answer 49

try 5/(7^2pi)ft/min. i am sure this is correct.

Answer 50

YES YES YES YES YES!!!!!

Answer 51

lifesaver @wynnwynn

Answer 52

Thank you very very much

Answer 53

:)