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
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
r = 2h/3
V = (1/3)π(r^2)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).
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