# Finding the minimal dimension of the length (Just give hints on each problem) Thanks

1. Nov 9, 2004

### eagle_johny

The Dome Tent

1 .Imagine making a tent in the shape of a spherical cap (a sphere with lower portion sliced away by a plane). Assume we want the volume to be 2.2 m^3, to sleep two or three people.

a. make a sketch of this tent, identifying all appropriate variables
The floor of the tent is cheaper material than the rest: assume that the material making up the dome of the tent is 1.4 times as expensive per square meter than the material touching the ground

b. determine and graph a function, which gives that cost of the tent material as a function of an appropriate variable

c. what should the dimensions of the tent be so that the cost of the material is a minimum?

d. what is the total area of the material used for this minimum cost tent?

e. now consider a dome tent in which the floor is more expensive than the rest of the tent material” assume that the material touching the floor is 1.4 times as expensive per square meter than the material making up the dome of the tent. Carry out steps a) b) and c) above for this tent

f. how practical would each of these two tents be?

so confusing