Ok so I tried using these formulas but I get a diff answer from the book

Ok so I tried using these formulas but I get a diff answer from the book

pi (r)^2h/3=10 r^2+h^2=L^2

piL^2-angle/2 (L^2)=surface area

Help please

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>Find equation for cone.
>differentiate expression with respect to radius and height
>set equal to zero.
>solve

Equation for volume*

My answers dont match the books and im starting to believe the book is wrong

Its not just the volume you need the surface area too

Same approach?

This should clear things up

Sorry man, I didn't read the problem properly.
Okay, so you know that there is a fixed volume right?
Look up the volume for a cone, combined with the fixed volume you have two varaibles left, height and radius.
Find the best ratio between the radius and height of the cup in the case of surface area.
Do you understand these first steps?

Bro

I have feeling dat angle you need to cut the paper is whats missing though the book has even went over differentiation of inverse trig functions so Im stuck trying to figure out if its relevant or not

Yeah just figuered out the angle can be related to the height and radious angle=2piL-2pir. Fucking problem just got way more tedious fuck

gimme a sec

Ok after working it out more the fomulas that are relevant are

angle*L=2piL-2pir

L^2=r^2+h^2

pi/3*h*r^2=10

Made a mistake on my first angle formula but now I got it

Got it

You have the right answer?

...

Yeah

I've got the same.
But I didn't used the angle.
Saved a couple of steps.

It was given that r^2=30/(pi*h) for a volume of 10 cubed centimeter.

For the surface area of the cone I used SA=pi*r*(r^2+h^2)^(1/2)

I substituted h and differentiated it with respect to r and set equal to 0.
Solved for r and got the same expression as you.

Yeah im sure pluging the angle formula in the Sa formula will give you the formula you used, I assumed that the area is smallest where the angle is greatest but yeah your formula looks way easier to differentiate, did you derive the formula yourself or did you look it up?

Looked it up.
Might be fun to try to derive it.

Suprisingly easy actually.

Angle=(2piL- 2piR)/L

piL^2-(angle/2)L^2=Sa

piL^2-(piL-piR)L=Sa

piRL=Sa

Lol and Ignored the Sa formula cause I thought the angle formula would be easier to work with

We always have to first find a general solution and only then apply it to a specific case. But that's modern homeschooling.. R=2.916cm and h=1.684cm I guess.
Why is the optimum cone angle exactly the same as the tetrahedral angle?

We learn something new everyday.

Only god knows

I will find out, inshallah.

Number 37 im 99 percent sure the book is wrong I get 3R for height and 3/2R for radious what do you get

Any ideas?