Question

A circular conical reservoir, vertex down, has depth 20 ft and radius of the top 10 ft. Water is leaking out so that the surface is falling at a rate of 1/2 ft/hr. The rate, in cubic ft per hr, at which the water is leaving the reservoir when the water is 8 ft deep is...

Answer 1

@tkhunny?

Answer 2

cmon guys please?

Answer 3

@amistre64

Answer 4

what is the formula for volume of a cone?

Answer 5

V=a^3

Answer 6

whoopps

Answer 7

thats a cube, we want a cone

Answer 8

1/3pir^2h

Answer 9

good, and we will also want to define the relationship between height of water and radius

Answer 10

i don't know how to do that

Answer 11

we know 2 points of reference: 0,0 and 10,20 for a given r,h

Answer 12

when we have 2 points, we can make the equation of a line

Answer 13

alright so slope=1/2, which we know

Answer 14

so r=1/2h?

Answer 15

h = 2r

V = 1/3 pi r^2 h

the rest is derivatives ...

Answer 16

where do i start?

Answer 17

with h or V we need the derivative of both of them to help us out

Answer 18

use implicits

Answer 19

h'=2, but what do i take the derivative of V=1/3pir^2h with respect to?

Answer 20

h r and V are all functions of time, so

h = 2r: h' = 2r'

V = 1/3 pi r^2 h: V' = 1/3 pi (2rr' h + r^2 h')

Answer 21

ask me why if that doesnt make sense

Answer 22

no, i get it, product rule, dr/dt/dh/dt right?

Answer 23

yep

Answer 24

ok

Answer 25

so, lets fill in the information

Answer 26

h' is given as: 1/2, and h = 8

h = 2r: h' = 2r'
8 = 2r: 1/2 = 2r'

fill in and solve for V'

V' = 1/3 pi (2rr' h + r^2 h')

Answer 27

h' might be better is -1/2 since it is falling

Answer 28

ok i think i understand

Answer 29

just gimme a min

Answer 30

1/3pi(24) ?

Answer 31

h' = -1/2
h = 8

r=4
r'=-1/4

fill in and solve for V'

V' = 1/3 pi (2rr' h + r^2 h')

V' = 1/3 pi (-2(4)(8)/4 - 4^2/2)

V' = 1/3 pi (-16- 8)

V' = -pi (8)/3

Answer 32

yea i think i messed up a negative somewhere because i got the same answer, but positive

Answer 33

think it had something to do with h=1/2

Answer 34

you were right, i see my error

Answer 35

rather than -1/2

Answer 36

-16-8 = -24

Answer 37

so it's -8pi?

Answer 38

V' = -pi (24)/3 = -8pi

the negative just tells us water is leaving the system

Answer 39

yea, i think get it now , thanks a ton! I'm trying to teach myself calc but it's really hard, help is greatly appreciated

Answer 40

i taught myself, so you should do fine

Answer 41

General Rule: Post YOUR work, and you get better answers, sooner.