Late afternoon brainteaser

[Anonymous No.4612245]

Hi /sci/, here is a brain teaser I presented to my Maths teacher. It took him a few minuets to solve, can you beat a Maths teacher?

A cylinder with a radius of 4x is not entirely full of water. The base of the cylinder to the water mark is h cm.

A sphere with a radius of 3x is dropped into the cylinder and the sphere is entirely submerged.

Calculate the change in h in terms of x after the sphere has been entirely submerged.


To get you motivated: This question is expected of a "high ability" 15 year old

[Anonymous No.4612263]

>This question is expected of a "high ability" 15 year old
And what makes you think is even remotely motivating?

[Anonymous No.4612280]

>>4612263

Just imagine that cocky 15 year old sitting at the desk in front of you celebrating that he got the answer correct and you are sat there not being able to do it- you would be motivated to try and do it, wouldn't you?

[Anonymous No.4612289]

>Too hard for /sci/

[Anonymous No.4612299]

>>4612289
>buttmad op that no one is doing his homework for him

[Anonymous No.4612307]

>>4612299
I know the answer and I will post it if no one is going to give this one a go

[Anonymous No.4612308]

>>4612280
Except that it is extremely easy, and a 15 year old is expected to be able to calculate the volume of a sphere and the volume of a cylinder, which is all there is too it.

[Anonymous No.4612311]

>>4612245

Too easy. Take <span class="math">V_sphere = V_disk[/spoiler]

(4/3)pi*(4x)^3 = 2pi*h (pi*((3x)^2)

h = x *4^4/ (3^3 *2pi)

Took longer to write it than to solve it.

[Anonymous No.4612313]

>>4612308

Then do it, bitch

[Anonymous No.4612321]

>>4612311
You can simplify the answer further than that

[Anonymous No.4612326]

If you need to find 4h you can just search their website for your local chapter.

[Anonymous No.4612332]

>>4612313
So I should do everything that is easy.
Does that include pointing out how butthurt you are that everyone thinks your "achievement" of solving this problem is actually a triviality?

[Anonymous No.4612333]

I got 2.25x = dh

It's not even really a brainteaser, you just set the cylinder volume equal to the sphere volume.

[Anonymous No.4612334]

>>4612321
and what the fuck is the point, you retarded high schooler?

once you get out of high school you will realize that no one gives a shit about simplifying answers, as it's a waste of time and provides little to no benefit.

[Anonymous No.4612340]

>>4612321

Do you want to try solving a real problem?

A cylinder of radius 1 and height 3 is imposed into a sphere of radius 1. Find the total volume of the intersection.

[Anonymous No.4612344]

>>4612333

We have a winrar>

>4612332

>Late afternoon brainteaser
>brainteaser
>Late afternoon

I just wanted to post a small little problem to see if anyone got the correct answer

[Anonymous No.4612346]

>>4612340
The volume of the sphere, because the cylinder completely contains it?

[Anonymous No.4612359]

>>4612346

Geez, that was awful on my part. Let the radius be 2.

[Anonymous No.4612366]

>>4612334

It's classed as incorrect in a "trivial" exam paper if you had it in that form, is all.

[Anonymous No.4612371]

>>4612359
Haha, yeah I was looking for the tricky part and couldn't find one. That's a fair bit more complicated now.

[Anonymous No.4612377]

>>4612334

Also check the picture

[Anonymous No.4612384]

what's so hard?

calculate volume of sphere and divide by (pi*r^2) to get the height difference in the cylinder.

fucking stupid problem.

[Anonymous No.4612388]

>>4612334
Well, seeing as how your answer is actually incorrect (the pi term cancels out, among other things) I'd say you are pretty over-mad about this.

[Anonymous No.4612392]

>>4612384

It's not hard, that's why I've called it a "Late afternoon brain teaser"

It's just supposed to be a bit of fun

[Anonymous No.4612405]

>>4612392

well it's a fucking stupid problem. can't you come up with one that's actually fun to do, like those probability ones with bayes or binomial distributions and a half-asses scenario?

the only thing this thread succeeded in teasing was the fatty buildup in my arteries due to elevated blood pressure

[Anonymous No.4612420]

>>4612334
Pic related

[Anonymous No.4612439]

>>4612405
>Statistics
>Fun
I shiggybannigyboodyroodydo

Just joking, I'll see if I can find something

[Anonymous No.4612443]

I think OP should show me how to derive the formula for the volume of a sphere.

[Anonymous No.4612451]

>>4612359
<span class="math">2(\int_{0}{1}\pi x^{2}dx) + \pi2\sqrt{3}[/spoiler]
<span class="math">=2\pi\frac{1}{3} + \pi2\sqrt{3}[/spoiler]
<span class="math">=\pi(\frac{2}{3} + 2\sqrt{3})[/spoiler]
I had a go.

[Anonymous No.4612465]

>>4612392
>brain teaser
>doesn't tease brain
eye c what your doing their

[Anonymous No.4612469]

>>4612451
That 1 in the first line is meant to be the upper bound of the integration.
And the link is meant to be >>4612340