Question

What shape best fits inside a sphere?

Answer 1

a slightly smaller sphere

Answer 2

Other than another sphere

Answer 3

what do they mean by "best fit"?

Answer 4

triangle @MathematicsNerd

Answer 5

or what are the answer choices @MathematicsNerd

Answer 6

Leaves the least volumee when inscribed inside the sphere

Answer 7

*volume

Answer 8

I think a cube: it is a problem of the maximum and minimum

Answer 9

Is there a way to explain why a cube works best?

Answer 10

well what are the possible choices... the more sides a polyhedron has the more it resembles a sphere

Answer 11

Yes I think, it'necessary going in two dimensions, namely a square enclosed in a circle

Answer 12

This is not a multiple choice question

Answer 13

possibly because theyre all 90 degree angles @MathematicsNerd

Answer 14

obviously the best fit is the polyhedron with maximum number of faces - i.e. the most like a sphere you can get without being a sphere

Answer 15

then i say a dodecahedron :)

Answer 16

What about out of these shapes: cylinder, pyramid, cube or rectangular prism, or cone.

Answer 17

*square pyramid

Answer 18

I think the statements is this: "among all quadrilateral of fixed perimeter enclosed in a circle, which is the quadrilateral, enclosed in a circle with maximum area of surface?"

Answer 19

ok now i say cube

prove it mathematically by assuming radius of sphere is 1
then side of cube is 1/sqrt2

Answer 20

** sorry side = sqrt(2)

Answer 21

@Michele_Laino did oyu just make that up? it is NOT the question asked.

Circles are not spheres. There is no restraint given on the shape.

If it is not a sphere, then it is the nearest thing to a sphere you can get (@dumbcow that is not a dodecahedron)

Answer 22

@MrNood please, note that I don't say the circles are speres, I only said that the question of @MathematicsNerd can be studied if we go in two dimensions as well, namely if we consider circles and square instead speres and cubes!

Answer 23

Look at the shape called a 'buckyball'

It is a series of hexagons making a ball.

I am not saying that his is the best fit (you just need more face) but it is EVIDENTLY better then cubes, pyramids etc.

Answer 24

@Michele_Laino
I doubt very much that yur assertion is true (I admit its possibility - but doubt you can prove it)

In any case even if it IS true then it is plain that a hexagon, octagon hexadecigon and millionagon are better fits than squares, triangle etc.

Answer 25

btw - I made up millionagon :-)

Answer 26

the proof is immediate, it is suffice to get the cross section with a plane passing through the centre of the sphere, and we get a circle within enclosed a square, both them have the centre located at the same point

Answer 27

that is plainly not true

A hexagon has occupies more of the circle , and by your reasoning (which I am yet to accept) would occupy more of the sphere in 3D

Answer 28

@MrNood you are right! that' true, before I have only indicate one possible solution, limitated to parallelepipeds.

Answer 29

@mathmaqticsnerd

I feel that your question is not really well defined. Whilst my answer above (milllionagon) is correct it is probably not the intention of your question.

Is there some restraint on the shape you want to to fit inside?

Is it a cuboid for instance?

Answer 30

@Michele_Laino but that restraint was purely invented by you and does not answer the OP question

Answer 31

@MathematicsNerd

I feel that your question is not really well defined. Whilst my answer above (milllionagon) is correct it is probably not the intention of your question.

Is there some restraint on the shape you want to to fit inside?

Is it a cuboid for instance?

Answer 32

(by millionagon - I mean 'maximum sided polyhedron that is not a sphere')