you have to design a space station (model) that has a 120 cm3 volume, and it has to have the possible smallest surface area. it must contain 3 different shapes. (cone and sphere surface are was not covered, only their volume, so they are out....we can calculate the area of rectangles,triangles, circle, area and surface of cylinder, cube, prisms, pyramids with those bases.. ) my guess is it has to have a cylinder body and at the two end a square based shape with the smallest height possible?

Question

you have to design a space station (model) that has a 120 cm3 volume, and it has to have the possible smallest surface area. it must contain 3 different shapes. (cone and sphere surface are was not covered, only their volume, so they are out....we can calculate the area of rectangles,triangles, circle, area and surface of  cylinder, cube, prisms, pyramids with those bases.. ) my guess is it has to have a cylinder body and at the two end a square based shape with the smallest height possible? 
I am still leaning to have on one end a sphere (half sphere, the same radius as the cylinder), even though we cannot officially calculate the surface, just based on the knowledge that the  sphere is the most "compact" shape and will have the smallest surface for sure, without actually calculating it.. 
but i do not know how to calculate to make it "the smallest possible" surface.. any thoughts? Please..

scott · Answer

if you google "cylinder minimum surface area" , you will find that a can whose height is equal to its diameter is the minimum surface area

a "most compact" sphere fits inside, touching the cylindrical wall and the two ends

ed · Answer

it has to be made out of 3 different shapes, though.I am not sure if i put shapes inside it completely,it will be acceptable..