Geometry + algebra

[storm sage]

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[zealous tulip]

As we know, l²=r²+h², let
r=3 cm and h = 4cm. Therefore,l will be 5 cm.
Using this formula, (πH²):
$$π(4)²$$
$$16π cm²$$
Now, using original formula for curved surface area of cone(πrl):
$$π(3)(5)$$
$$15π cm²$$
But, 15π≠16π.

[fresh shadow]

Infinite.......

[zealous tulip]

Check this before checking the actual question

[austere kraken]

what

u took $r=h$ for getting $\pi H^2$ but the $r$ and $h$ you assumed are not equal because $3 \neq 4$

[fresh shadow]

wolfqz

[zealous tulip]

Bro when a cone make a circle its(cone's) height is equal to Radius of the circle.

[grizzled peak]

no it won't lol

[zealous tulip]

Here, original formula is 'curved surface area of cone '

[zealous tulip]

Why ?

[grizzled peak]

the CSA of a cone is part of a circle with radius l

where l is the slant height

[grizzled peak]

or a sector uwu

[zealous tulip]

Ok, if I find the area of circle with radius l,will I get the curved surface area of cone?

[grizzled peak]

radius what

[zealous tulip]

L

[grizzled peak]

no

[zealous tulip]

Then ?

[grizzled peak]

you have to do pi*r*l

do you want a derivation of it?

[zealous tulip]

No, I know its derivation

[grizzled peak]

alr

[zealous tulip]

But why I can't use π(H)²

[grizzled peak]

because your assumption of H is wrong

and

well

just no

the CSA of a cone is NOT a circle

it is a sector

so it's formula would be

[zealous tulip]

Are you Indian ?

[grizzled peak]

$\frac{\pi l^2 \theta}{360}$

[fresh shadow]

Inverse Cupid #GTFOanemia

[grizzled peak]

yes

[zealous tulip]

Can I ask in Hindi

[grizzled peak]

no

i am not good at hindi

[zealous tulip]

Ok, then you won't understand my question.

[zealous tulip]

What !

Being an Indian,how can you say this ?

[grizzled peak]

oh i get it

ah

[zealous tulip]

?

Understood?

[grizzled peak]

rolling the cone on the ground would make a circle, yes
but the area of this circle IS NOT the CSA

[zealous tulip]

Yes, but why ?

[grizzled peak]

ok, as you know, a circle is basically 360 degrees

[zealous tulip]

Yes

[grizzled peak]

right?

now

let's take a simple example

with radius as 1

slant height as 2

height as sqrt(3)

so the circumference of the base is 2pi

[zealous tulip]

You continue, I am coming back in two minutes

[grizzled peak]

right?

and the circumference of the circle with radius l is 4pi

but the CSA wraps around a length of 2pi

[zealous tulip]

Wrong !

[grizzled peak]

so we wish to find the area of the resultant sector given the arc surrounding it is 2pi

l is 2

h is sqrt(3)

bruh

[zealous tulip]

Sorry

I didn't see sqrt

Sorry...

Continue

[grizzled peak]

eh it's fine

[grizzled peak]

now I know there's a formula for this

but let's find theta

we can do that by doing $\frac{2\pi\times 360}{4\pi}$

[fresh shadow]

Inverse Cupid #GTFOanemia

[grizzled peak]

which gives 180

[zealous tulip]

Wait...

[grizzled peak]

so when we flatten out the CSA of our cone

[zealous tulip]

What are we finding...

[grizzled peak]

we only actually get HALF of the circle that you said is the CSA

[grizzled peak]

angle of the sector formed by the CSA
assuming that the CSA is part of a circle with radius l

[zealous tulip]

Why sector ?

Sector is used in circles (which is 2-D) but here cone is 3-D !

[grizzled peak]

alr, I'll tell you someth to do
make a cone yourself

draw a line from it's vertice on the top to any random point on the circumference of the base

then roll it

make sure you roll it when the line is on top

see how many times the line appears on the top again in a full rotation

[zealous tulip]

Yes, when it covers 1 complete revolution it's its CSA

[grizzled peak]

nope

[zealous tulip]

Yes

?

[grizzled peak]

the line will appear again at least once

if you want a measurement of it

[zealous tulip]

Yes

[zealous tulip]

Yes....

¿

[grizzled peak]

$\floor{\frac{l}{r}}$

[zealous tulip]

?

[fresh shadow]

Inverse Cupid #GTFOanemia

[grizzled peak]

yeah that's it

[zealous tulip]

What is this?

[grizzled peak]

amount of times this line reappears on the top in one full rotation

[zealous tulip]

Oh then ?

[grizzled peak]

for your theory to be correct

l/r has to be 1

or in other terms

[zealous tulip]

R=l

[grizzled peak]

the line has to reappear on the top at the exact moment one whole revolution is completed
and the line only appears once

[grizzled peak]

yeah

and h = 0

for your method to be correct

[zealous tulip]

That is impossible

[grizzled peak]

that's it

[zealous tulip]

Oh thanks

@grizzled peak

[grizzled peak]

you're welcome

[zealous tulip]

Should I close ?

+close