A square bottomed pyramid is placed inside a sphere. What is the ratio of the volumes...

A square bottomed pyramid is placed inside a sphere. What is the ratio of the volumes, assuming that the pyramid has the highest volume possible?

I enjoyed this one. Thought I'd share it here.

Other urls found in this thread:

en.wikipedia.org/wiki/Square_pyramid
mathworld.wolfram.com/SquarePyramid.html
en.wikipedia.org/wiki/Ratio
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Wasnt as hard as I thought it would be

>square bottomed pyramid

That is just called a quadrilateral pyramid.

>how to find function maximums

Square bottomed pyramids make the rocking world go round

Stop calling it that. Read a book about solid geometry and learn all the real kewl as fuq names.

>don't call a square pyramid a square pyramid
>just call it a quadrilateral pyramid with a parallel and equilateral base
Also, it is called a square pyramid.
en.wikipedia.org/wiki/Square_pyramid
mathworld.wolfram.com/SquarePyramid.html

not enough information OP

what is the size of the lateral line?

OR

is the size of the side triangle the same of the side of the square?

>assuming that the pyramid has the highest volume possible

the ratio could be anything if he doesn't give at least two different measures of the pyramid

nice try retard

en.wikipedia.org/wiki/Ratio

the ratio is different depending on the measures of the pyramid you double nigger

there's only one (1) largest inscribed pyramid
it's only dependent on the radius of the sphere

Yes, there is enough information. You just need to understand that the radius of the sphere is constant.

So, what's the answer?

OP here, the answer is 16/27π
in case anyone was wondering.

>Also, it is called a square pyramid.

Actually, it is called a regular quadrilateral pyramid.

But a regular quadrilateral is also called a square so I will give you that. That said, you did not call it a square pyramid, you called it a square bottomed pyramid. Euclid is rolling in his grave.

yup, I did sphere to pyramid
Vs/Vp=(4/3)π/(8/9)^2=(27/16)π

post solution pls

Differentiate and equate to zero, it's like baby calculus

That's the least difficult part.
You obviously didn't solve it.