Question

You want to make cylindrical containers to hold 1 liter using the least amount of
construction material. The side is made from a rectangular piece of material, and this
can be done with no material wasted. However, the top and bottom are cut from squares
of side 2r, so that 2(2r)^2 = 8r^2 of material is needed (rather than 2πr^2, which is the total
area of the top and bottom). Find the dimensions of the container using the least amount
of material, and also find the ratio of height to radius for this container.

Answer 1

You want to make cylindrical containers to hold 1 liter
using the least amount of material.

The side is made from a rectangular piece of material,
and this can be done with no material wasted.

However, the top and bottom (circle) are cut from squares of side 2r,
so that 2(2r)^2 = 8r^2 of material is needed

Find the dimensions of the container using the least amount of material, and also find the ratio of height to radius for this container.

well, the width of the side rectangle is equal to the circumference of top/bottom pieces

that reduces the setup tp a degree

Answer 2

can you construct a material equation with this?

Answer 3

I can, but I'm confused with the part : "the top and bottom are cut from squares of side 2r, so that 2(2r)^2 = 8r^2 of material is needed (rather than 2πr^2, which is the total area of the top and bottom)"

Answer 4

it seems to be a constraint such that the result is pi r^2 = 4 r^2 yeah, thats odd to read