Question

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A water-filledspherical tank with a radius of 1 meter empties frm a hole in the bottom in such a way that the water level decreases at a constant rate of 3 centimeters per second. How fast is the volume of water in the tank changing when the tank is half full?

Answer 1

Hey Algebraic?

Answer 2

Since @Algebraic! started, I'll wait to see if she's teaching.

Answer 3

@calculusfunctions I don't think she is here.

Answer 4

Are you sure? It shows that she's typing.

Answer 5

She has been typing for the past 10 minutes since ive posted for help.

Answer 6

We need V in terms of h
start with a sphere radius R centered at (0,R)

It's possible they give you this expression in your text. I don't know, but that's where it comes from...

Answer 7

I can teach so that you can get the answer your self but I don't want to interrupt her.

Answer 8

Nvm..

Answer 9

server keeps refreshing the page, so what I've typed gets wiped.

Answer 10

Oh gotcha. I was just given the text and no pcture.

Answer 11

@Algebraic! I know what you mean. I have this problem constantly, where I'm almost done and have to start the whole thing over again. Annoying!

Answer 12

there's V(h), differentiate with respect to time.... plug in your known values (h and dh/dt ..make sure units agree: meters and meters/sec)

Answer 13

I know the formula for volume is \[V=4/3\pi r^3\]

Answer 14

Should i change meters to cms or cms to meters?

Answer 15

that formula isn't going to be directly useful here... because you are talking about the volume of the tank in terms of the height of the fluid...

Answer 16

yep.