If the maximum number of identical cylinders, standing upright and tou

Hi Shank18,

what does the main statement mean..

identical cylinders, standing upright and touching the edges..
same radius , the circular portion is base

can be fit into a rectangular box with a square base...
the base of rectangular box is square, so if x cylinders are placed along a side of base, the length of base is \(DIA*x=2rx\) and area of base = \(4r^2x^2\)
and volume will depend the side of base and height = \(4r^2x^2*h\) so THREE variables

let us see the statements-

(1) The radius of each cylinder is 5 centimeters.
Nothing about x and h
insuff

(2) The height of the box is 80 centimeters
nothing about r and h
insuff

combined..
total number is 200..

I. let the square base be of 10 cylinders.. so x=10, r=5 and h=80
so 10*10 =100 on the base and therefore another 100 on top of these 100, so volume = \(4r^2x^2*h\), where h=80..thus height of cylinder=40, as 2 cylinders fit in standing upright
\(4r^2x^2*h=4*25*10^2*80=800,000\)

II. let the square base be of 5 cylinders.. so x=5, r=5 and h=80
so 5*5 =25 on the base and therefore another 7 sets of 25 on top of these 25, so volume = \(4r^2x^2*h\), where h=80..thus height of cylinder=80/8=10, as 8 cylinders fit in standing upright
\(4r^2x^2*h=4*25*5^2*80=200,000\)
so different volumes possible, which will depend on the height of cylinder
insuff

E