Question

Related rates problem.... pictures below

Answer 1

where? @sleepyjess

Answer 2

your offline :/

Answer 3

Question:
A container in the form of a right circular cone (vertex down) has radius 4m and height 16m. If water is poured into the container at the constant rage of 16m^3/min, how fast is the water level rising when the water is 8m deep?

Answer 4

What I have so far
I know I need V in terms of h, but not sure how to get it to that

Answer 5

I'm just on the app, so it shows me offline

Answer 6

oh ok :)

Answer 7

find the value of radius when the height is 8m
differentiate the volume with respect to time
plug in the stuff and get dh/dt <-rate of change of depth

Answer 8

Once I get V in terms of h, I think I'll be fine. It's just getting the r gone and made into a form of h

Answer 9

you can write the radius in terms of height

Answer 10

How do I get the value of the radius if I don't know the volume when h is 8?

No, not familiar with integral yet

Answer 11

Agent, can't see drawing on the app...

Answer 12

Use similar triangles to find a relation between r and h.

Answer 13

Use similar triangles to find a relation between r and h.

Answer 14

Would r be 2 when h is 8?

Answer 15

First you have to find a way to express your volume only in terms of h, using the above.

Answer 16

That's where I'm having trouble

Answer 17

hint:use trigonometry

Answer 18

I have v = 1/3r^2*8, do I need to differentiate that or did I mess up somewhere?

Answer 19

Do not plug in any numbers yet. You have to differentiate before plugging anything in.

Look at the pic I attached. Remember similar triangles?

Answer 20

Or use http://i.imgur.com/CL7Kjkh.jpg

Answer 21

Yes, using the similar triangle, I got r = 1/4h. I can put that in before differentiating right?

Answer 22

Yes, you just can't plug in any values till after differentiating.

Answer 23

Okay, I plugged the 1/4h in and simplified it to 1/12pi h^3

Answer 24

Wait, I need to square the 1/4 first

Answer 25

I think I messed up somewhere...

Answer 26

hmmmmm

Answer 27

I got 16/4pi as the answer

Answer 28

Simplified to 4/publix

Answer 29

4/pi lol

Answer 30

you may be right....But don't take the word from me.........I need someone to approve 100%

Answer 31

lol publix

Answer 32

@mayankdevnani

Answer 33

@inkyvoyd @skullpatrol

Answer 34

looks right.....

in summary

\(V = \pi r^2 \dfrac{h}{3}\)

\(h = 4r \implies V = \dfrac{\pi h^3}{48} \)


\(\dot V = \dfrac{V}{dh} \dot h\)

\( = \dfrac{\pi h^2}{16} \dot h\)

\(\implies \dot h = \dfrac{16 \dot V }{\pi h^2}\)


\(= \dfrac{16 \cdot 16 }{\pi ~ 8 \cdot 8} = \dfrac{4}{\pi}\)

Answer 35

Don't forget units... you too @IrishBoy123

Answer 36

what are they?!?!

0.o

Answer 37

lol m/min