Dr. Jeff's Blog on the Universe

THE SOLUTION TO Weekly Challenge 6: Today’s Special in the Cosmic Kitchen is …

Posted by DrJeff on August 24th, 2009

Filed under 1.1. Dr. Jeff's Weekly Challenge, 1.2. Solutions to Weekly Challenges, 4. The Earth, 5.6. The Universe

Read Original Challenge HERE.

This post is a Dr. Jeff’s Weekly Challenge.

Welcome humans nice folks. We have assumed you are here for the answer to Weekly Challenge 6. Men in black team #26,342 is therefore now en route to your home. If you don’t know why, before reading any further we recommend (with great strength) that you read Weekly Challenge 6. Our team is rolling (very fast).

And now the answer—

Last week in the Cosmic Kitchen, Chef Jeff pushed the green button on the pasta press, and a single strand of Earth spaghetti was created that just stretched across the 93 billion light-year diameter of the observable universe.

What was the diameter of the spaghetti required? 1 millimeter (0.04 inches)

It is not microscopically thin. It is not the diameter of a fire hose. It is precisely the diameter of—angel hair pasta, a thin spaghetti. Go to your local store buy a box and measure it for yourself. By the way, help support us by purchasing our sponsor’s brand of angel hair. Look for Cosmic Kitchen Pasta #42 available in most supermarkets.

We also submit for your consideration that this was not magic, or some remarkable coincidence. In the Cosmic Kitchen we have the ability to realign the laws of nature. In this case, we have ensured that the Earth, when squeezed into a single strand of Earth spaghetti capable of spanning the observable universe, has the thickness of … spaghetti. We hope you humans nice folks appreciate the effort. We wanted your planet to still be recognizable to you, at least as today’s special entree.

We also hope you have enjoyed your visit to the Cosmic Kitchen. Its existence is a closely guarded secret, and we are honored to have shared it with you. The men in black will be knocking on your door at any moment. Won’t you please help them fill out our survey? And remember that you can receive a special gift if you answer their final question correctly. Since we have spent this last week together, I now consider us friends, and I want to see you receive your special gift. So remember I gave you the answer to the question last week. Just say “cheese.”

How did Chef Jeff come up with the answer?

The volume of the Earth, a sphere, is to be transformed into the volume of a strand of spaghetti, a cylinder. Recognizing that the volumes are equal, here is how it is done:

1. The volume of a sphere is: 4/3 x pi x R³ where:

pi = 3.14

R is the radius of the sphere, in this case the radius of Earth:

6,378 km = 6.378 x 10⁶ meters

2. The volume of a cylinder is: pi x r² x h where:

r is the radius of the cylinder, here the radius of the spaghetti, which is to be calculated

h is the height of the cylinder, here the length of the spaghetti:

93 billion light-years = 9.3 x 10¹⁰ light-years

converting to meters (see hint last week):

9.3 x 10¹⁰ light-years x 9.46 x 10¹⁵ meters / light-year = 8.8 x 10²⁶ meters

3. Setting the two volumes equal yields the equation (note the pi cancels out):

4/3 x R³ = r² x h