Need help pls Integral

[floral shoal]

<@&286206848099549185> PLS

[pearl sand]

So we have a sphere with 4cm radius and a hole into the sphere was drilled. The hole has a radius of 1cm. All right

What formula do you know for the volume of a sphere?

[floral shoal]

R=4,r=1

the only thing that I dont understand is what is the +h and -h

[pearl sand]

So you actually have to integrate

[floral shoal]

exactly

[pearl sand]

oh ok

I would need to show a picture

[floral shoal]

ok

[pearl sand]

do I get your agreement sir?

[floral shoal]

yes

I dont understand, do I send a picture ?

[pearl sand]

no me wait

This is what I think is going on

The blue one is the ball and the red is the whole

subtracting both from each other gives us basically a new ball with radius h

[floral shoal]

this is the picture with the problem

[floral shoal]

ok

[pearl sand]

What I don't get is it says h² = R² - r²

and I though it would be h = R - r

[floral shoal]

same thing

so h=3

[pearl sand]

I'd say so

$\int_{y=-h}^{y=+h} \pi(x^2-r^2)dy$ you should use?

[civic schooner]

adonhs

[floral shoal]

yes

[pearl sand]

I mean if we integrate by y then we need something with y

x² + y² = r²

x² = r² - y²

[floral shoal]

and x^2=15 and r^2=1

[pearl sand]

from where is that

is this the solution of the task?

or a hint?

[floral shoal]

Its what I have to do

[floral shoal]

yes

[pearl sand]

ok...

[floral shoal]

Look what I did

[pearl sand]

yeah my neck broke

[floral shoal]

I just dont know what is h+ and -h

[pearl sand]

,rotate

[pearl sand]

well let's ignore our skepticsm

it says h² = R²-r²

[floral shoal]

ok

[pearl sand]

then it follows $h = \sqrt{R^2-r^2}$

[civic schooner]

adonhs

[floral shoal]

yes

[pearl sand]

why is x² = 15?

why is y = 1?

[floral shoal]

4 square + 1 square = 15

My friend just tell me what to do without my picture

[pearl sand]

ok

I would substitute x² = R² - y²

[floral shoal]

ok so we dont have the y

[pearl sand]

no so we dont have the x

[floral shoal]

okok

so the x would be 4 square - y square

[pearl sand]

i need to think

can we ignore the solutions formula

[floral shoal]

yes

[pearl sand]

it just doesnt make sense to me

[floral shoal]

try something

[pearl sand]

Ok I read your French Solution so they substituted

why didnt you tell me

$\int_{y=-h}^{y=+h} \pi(R^2-y^2-r^2)dy$

[floral shoal]

what do u mean

[civic schooner]

adonhs

[pearl sand]

On remplace bien sur x² = R² - y²

[floral shoal]

are u french

[pearl sand]

no i am guy who used translator

Let's rewrite the bounds too

[floral shoal]

where did u find the solution

[pearl sand]

$\int_{y=-\sqrt{R^2-r^2}}^{y=+\sqrt{R^2-r^2}} \pi(R^2-y^2-r^2)dy$

[civic schooner]

adonhs

[pearl sand]

I stole it from your teacher

[floral shoal]

[pearl sand]

Can you integrate this it's simple

[floral shoal]

I dont have a teacher

[pearl sand]

ok main character

[floral shoal]

ok so like I said the solution is \int _{-\sqrt{15}}^{\sqrt{15}}:\pi \left(\left(4^2-y^2\right)-1^2\right)dy

my friend its the same thing

[pearl sand]

mon frere ok

So R = 4 and r = 1

[floral shoal]

and its equal 20\sqrt{15}\pi

[pearl sand]

$I = \int_{y=-\sqrt{15}}^{y=+\sqrt{15}} \pi(16-y^2-1)dy = \pi \int_{y=-\sqrt{15}}^{y=+\sqrt{15}}(15-y^2)dy \ \= 15\pi y - \frac{\pi}{3}y^3 \bigg |_{-\sqrt{15}}^{\sqrt{15}}$

[civic schooner]

adonhs

[pearl sand]

Is there a mistake?

[floral shoal]

its 20 But ty sir

[pearl sand]

thats y im asking

[floral shoal]

?

its y there

[pearl sand]

$=15\pi \sqrt{15}- \frac{\pi}{3}(\sqrt{15})^3 - 15\pi (-\sqrt{15}) + \frac{\pi}{3}(-\sqrt{15})^3$

[civic schooner]

adonhs

[pearl sand]

$=20\pi\sqrt{15}$

[civic schooner]

adonhs

[pearl sand]

I found the mistake

there was a minus instead of plus

$=20\pi\sqrt{15} \approx 243.346$

[civic schooner]

adonhs

[pearl sand]

which is insane

if you did this with a sphere and cylinder formula you get

[floral shoal]

Exactly thank you sir

[pearl sand]

,w V = 4/3pi4^3-pi1^2*8

[civic schooner]

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Requested by adoniszgks

[pearl sand]

242.94

it's really close

bonjour gojo

[floral shoal]

bonjour XD

[pearl sand]

oh i meant merci