Need help on derivative applications

[finite belfry]

An evil scientist is draining blood from a person's body to a right isosceles-shaped cone tank (peak vertex at right angle). The blood level in the tank is rising at a rate of
1 cm/s. At what rate is the blood volume increasing when the tank contains 9π cm³ of blood?

[latent storm]

1. Do not ping the Moderators, unless someone is breaking the rules.
2. Do not ping the Helper Moderators, unless there is a conflict between helpers.
3. Do not ping other members randomly for help.
4. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
5. Wait patiently for a helper to come along.
6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[ember pebble]

here, you’re meant to find dV/dt, and you’re given dh/dt and V

[finite belfry]

yea

but idk how

[ember pebble]

set up an equation for V first.

to be precise, use the volume of a cone formula, then since you’re given V, dh/dt, and and r (since it isosceles) we can use the formula

[finite belfry]

V = ⅓•pi•r²h

then?

how to take derivative cuz there are 2 variables r and h

[supple isle]

So then you have to find one as a function of the other.

[finite belfry]

r as a function of h?

[supple isle]

That would make sense, given you know dh/dt.

[finite belfry]

but how

[supple isle]

...use the information you're given.

[finite belfry]

how to find their relation

[supple isle]

what information have you been given?

[finite belfry]

right-isosceles shaped cone tank

[supple isle]

Okay.

[finite belfry]

peak vertex at right angle

[supple isle]

So how do we use that?

[finite belfry]

i have trouble visualizing it

[supple isle]

You know what a right isosceles triangle is, right?

[finite belfry]

yea

[supple isle]

It's the 45-45-90 triangle.

[finite belfry]

ahh

wait

so r = h?

[supple isle]

Yep.

But show your work.

[finite belfry]

@supple isle

[finite belfry]

so V = ⅓•pi•h³

?

[supple isle]

I'm not sure how that proves what you're saying.

[ember pebble]

what?

[finite belfry]

i divide the triangle into 2

then become 2 smaller isosceles right triangles

[supple isle]

Why?

[finite belfry]

wdym why

[ember pebble]

(also, just as a side note, please be clearer with your wording, it helps the helper to understand your reasoning)

[supple isle]

I mean, why does that happen?

[finite belfry]

similarity maybe?

[supple isle]

You shouldn't use "maybe" in math.

[finite belfry]

i mean

its isosceles

so the height divides the triangle into 2

the base

and the 90 angle

so the smaller triangles r also isosceles

[supple isle]

You're not communicating an actual chain of logic, just a series of disjointed unconnected ideas.

[supple isle]

@finite belfry

[unique haven]

@finite belfry

<:HelpIcon:1304095958283321385>| Help Reminder

Hello thelolzbot4, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.