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/sci/ - Science & Math

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1786118 No.1786118 [Reply] [Original]

Sup homework, please excuse my mental retardation, but how might I go about finding the volume of the pink wedge? It's a plane at 45 degrees intersecting a cylinder of radius r at the diameter of the base. The calculus is simple enough, but I suck at algebra. How do I go about figuring out the cross sectional area?

>> No.1786126

>>1786118
>The calculus is simple enough, but I suck at algebra.

WTF am i reading? You r good at cal, but suck at algebra? WTF?

>> No.1786131

>>1786118
Im good at sentances, but suck at words...lol

>> No.1786132

I can believe it. I've met a mathematician who sucks at algebra but excels in set theory.

>> No.1786140

http://lmgtfy.com/?q=figuring+out+the+cross+sectional+area

>> No.1786144

Get the area of the semicircle (1/2 pi.r^2), then get the vertical cross section integral with calculus and multiply them.

I think that's how it works, but my calculus doesn't extend to solid volume.

>> No.1786153

>>1786126
It happens man, I suck at figuring shit like the formula for cross sectional area out. But once I get that, then integrating that shit and calculating the volume is no sweat. Maybe it's geometry I suck at and not algrebra? Fuck if I know.

>> No.1786154

get volume of cylinder, cut valium of cylinger in half, then take a fourth of that, assuming the pink area's halfway up the cylinder??? sorry, i'm going back to /b/...

>> No.1786157

GUYS. How about cross-sections going the OTHER way? Cross-sections shaped like triangles. It's a LOT simpler.

Here's the solution, don't read it if you don't want me to spoil the answer:

2*Integral from 0 to r: 1/2(r^2-x^2)
((r^2)r - (r^3)/3) = (2/3)(r^3)

>> No.1786170

>>1786154
Cutting a semicircle that way gives you non-congruent pieces, so no. Not bad thinking though.

>> No.1786174
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1786174

>>1786132
Yeah, you can suck at "algebra". But the Algebra the OP is talking about is really "Arithmetic", not " algebra". You need basic arithmetic to do calculus and just about every branch of math.

You cannot suck at arthmetic and do calculus.

>> No.1786176

>>1786154
Lol, I was thinking along a similar line, like get the volume of the rotation about the y axis of y=x from 0 to r and halving it, but it's not the same.

>> No.1786189

>>1786174
But algebra is the mathematics of generalized arithmetical operations...

>> No.1786193

>>1786157
Derp, why the hell didn't I see that?? Thanks anon.

>> No.1786208

ok so that's NOT 1/8 the volume of a cylinder???

>> No.1786215

>>1786208
Take that piece, make an exact copy of it and then try making a semicircle with it by joining them.

Problem?

>> No.1786234

sorry i don't know latex
integrate z(0->r/cos(45) r(0->r) theta (-pi/2-> pi/2)
r^3 drdzdtheta
i'm tired as hell and this is probably wrong

>> No.1786255

>>1786215
oh wow you're so right fuck!!

>> No.1786310

>>1786234
I'm 12 and what is this? Sounds too complicated, all I need is <span class="math">frac{1}{2}\int_-r^r\left(\text{r}^2-\text{x}^2\right)\text{dx}<span class="math">
Sorry if that doesn't come out right, I dunno what I'm doing lol.[/spoiler][/spoiler]

>> No.1786314

<span class="math">frac{1}{2}\int_-r^r\left(\text{r}^2-\text{x}^2\right)\text{dx}[/spoiler]

>> No.1786317

>>1786314
>>1786310
Fuck it, I don't how this latex shit works.

>> No.1786323

Damnit, one last try lol.
<span class="math">frac{1}{2}\int_-r^r\left(r^2-x^2\right)dx[/spoiler]