What's wrong with this /sci/? Why I am getting the last

>>7728812

well to begin with you're assuming that P = 2pir = one anus

it's actually two ani

insert that into ur equation f a m

>>7728818
>it's actually two ani

what? isn't the perimeter of a circle 2·pi·r ?

>>7728812
Think shells

V= ∫[0,R] 4πr^2 = 4/3πR^3

For disks

V=∫ π √[R^2-r^2]^2 dr = π ∫ R^2-r^2 dr = 2π[R^3-R^3/3]=4/3πR^3

>>7728822

i'm just shitposting

math is hard

>>7728812
well try to look at what you're integrating, you're not doing the same thing as before. The volume you're calculating is that of two cones glued together (dr varies linearily).

Try integrating the surface of spheres from 0 to R.

>>7728828
> you mean, this? V=2·∫[0,R] π·r^2 It's the same result

>>7728833
no I don't mean this.
That's what you're doing in the OP, which is false as I said because you are calculating the volume of two fucking cones.

I mean what >>7728826 said with shells. Or by taking into account the curvature of the sphere if you want to integrate disk surfaces.

>>7728843
thanks anon

>>7728812
that is the right answer, except that r should be R. the equation and the picture are for the volume of a solid formed by combining two right, circular cones, each of radius R and height R.

>>7728812
you are thinking it wrong

think of a single "p" which rotates of 180°
or half "p" that rotates of 360°

Please post more pictures like that, with new shapes being formed by integrating the previous ones.
Gives a very nice perspective.

here >>7729195
I assumed you were calculating the surface, that's what the draw is.
for the volume you have to use the surface and integer from 0 to R
pretty easy