1000 cu ft per unit, 280 m units; find radius of sphere that

A

afritts1987

New member
Joined
Sep 18, 2008
Messages
10
You propose to build a space ship that allows the entire population of the United States (280 million) to leave the earth. Your plans allocate an average space of 1,000 (= 10 x 10 x 10) cubic feet to each person.Your space ship is going to have the shape of a sphere. What is the radius of your space ship?

------------------------
Ok so I used the Volume formula of a sphere which is V= 4/3pir^3. But I was confused as to where to plug in the 1,000. I first put the whole volume equation equal to 1,000 but came out with a small number (like 3.1 or something) and I know it should be a BIG number. Do I need to include the number of the population in the problem? If so where do I put it?
 
Re: Volume of a Sphere Word Problem

I'm a little puzzled about the space design. Are you trying to stuff cubes into a giant sphere? If we can squish things so that there is no wasted space, this is not a very tricky problem. If we are stuck with an individual space design, this is a problem of great complexity.
 
Re: Volume of a Sphere Word Problem

afritts1987 said:
You propose to build a space ship that allows the entire population of the United States (280 million) to leave the earth. Your plans allocate an average space of 1,000 (= 10 x 10 x 10) cubic feet to each person.Your space ship is going to have the shape of a sphere. What is the radius of your space ship?

------------------------
Ok so I used the Volume formula of a sphere which is V= 4/3pir^3. But I was confused as to where to plug in the 1,000. I first put the whole volume equation equal to 1,000 but came out with a small number (like 3.1 or something) and I know it should be a BIG number. Do I need to include the number of the population in the problem? If so where do I put it?
Click to expand...

The problem can get very complicated - but I think the problem designer was looking for simple multiplications and divisions - and cube roots.

How much volume would it take to stuff 280 * 10[sup:1edezdv7]6[/sup:1edezdv7] people = 280 * 10[sup:1edezdv7]9[/sup:1edezdv7] cuft.

This is the minimum volume of sphere required.

Now use the volume formula and find the minimum radius.
 
Re: Volume of a Sphere Word Problem

Right, either that or (280000000)^(1/3) = 655, rounding up.

This makes a cubic structure of cubes, exactly 655 cubes to a side.

What's half the diagonal of the giant cube? You had better pad those sharp corners.

Note: 655^3 = 281011375, so you would have over one million empty cubes! (Assuming 280 million was within about 12,000 to an exact value.)

Note: If you leave about a quarter million who aren't worthy to make the trip, you can get away with 654 to a side. Contoversy! How do you decide who is worthy? :evil:
 
You must log in or register to reply here.
Top