Calculus
posted by Katie on .
If water is poured into a cup at a rate of 1 cubic centimeter per second, how fast is the dept of the water increasing when the water is 4 cm deep?
r = 6 cm
h = 9 cm
V = 1/3(pie) r^2 x h
V = (pie)r'h + 1/3 (pie)r^2 h'
6 / 9 = r / h
6h = 9r
r = 3 / 4.5 h
V = 1/3(pie) (3/4.5h)^2
My answer came out to 9 / 64(pie) cm/sec.

what is the shape of the container?

The shape is a cone. The radius is 6 cm and the height is 9 cm

Your answer is correct if you write it as
9/(64pi).
I am curious why you went from
6h = 9r to
r = 3/4.5
why not just do
r = 6h/9 = 2h/3
instead of having decimals in your fraction.
Either we use fractions or we use decimals, but we generally don't mix them together. 
I think you have a mistake. I was working on this problem at the same time.
V = 1/3 pi r^2 h
Only 'r' is squared. It appears that you squared 'h' too.
V = 1/3(pie) (3/4.5h)^2
Anyway, even with squaring h too, I don't come up with 9/64 pi. 
Here is what I did
from above
r = 2h/3
V = (1/3)π(r^2)h
= (1/3)π(4h^2/9)h
= (4π/27) h^3
dV/dt = (4π/9)h^2 dh/dt
when dV/dt = 1 and h = 4
1 = (4π/9)(16)dh/dt
dh/dt = 9/(64π)
(notice that Katie had r = 3h/4.5 which I found strange since that is simply 2h/3 ) 
I used r = 2/3 instead of r = 2/3 h!
Thanks so much REINY.
I really appreciate you taking the time to explain this to me.
I am teaching myself calculus, and sometimes the book just doesn't explain things well.
The r = 3h/4.5 threw me at first, until I figured out what she did (I had 2h/3).