Water is slowing at the rate of 50m^3/min from a concrete conical reservoir of the base radio us 45m and height 6m
How fast is the water level falling when the water is 5 m deep? Give answer in cm/min

Question

Water is slowing at the rate of 50m^3/min from a concrete conical reservoir of the base radio us 45m and height 6m
How fast is the water level falling when the water is 5 m deep? Give answer in cm/min

kayders1997 · Answer

https://www.twiddla.com/2552688

kayders1997 · Answer

I'll show work on what I did on there

danjs · Answer

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danjs · Answer

$$V = \frac{ 1 }{ 3 }*\pi*r^2*h$$

kayders1997 · Answer

I have a question

kayders1997 · Answer

I called the height 6 but wouldn't that h have to be 6-h than?

danjs · Answer

Find:  dh/dt

Write the volume in terms of just h by using similar triangles to relate r and h.
$$\frac{ 45 }{ 6 }=\frac{ r }{ h }$$
$$r=\frac{ 45 }{ 6 }*h$$

kayders1997 · Answer

Why wouldn't it be 6-h?

kayders1997 · Answer

Oh wait

danjs · Answer

the entire height is 6m,  the arbitrary height is h for the smaller triangle

danjs · Answer

Now you have a relation between r and h by similar triangles... put that r into the Area

$$A = \frac{ 1 }{ 3 }*\pi*(\frac{ 45 }{ 6 }h)^2*h$$

Simplify that and take the time derivative of the whole thing

kayders1997 · Answer

But if It was for the large one and the small one was 6 it would be h-6 than? For that part of the height

kayders1997 · Answer

I'm sorry if I'm confusing you

danjs · Answer

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