Slicing a sphere

Geometry Level 4

What is the maximum number of solid parts (not necessarily equal) a sphere can be divided into by 100 planes?

404253 501501 166751 970200 646800

Ossama Ismail by Ossama Ismail , 63, Egypt

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Aniruddha Bagchi
Jan 29, 2017

As we can use the Lazy Caterers' Sequence to deal with the cutting of 2D circles , in the same way we can apply that to a 3D sphere and solve this question.The 3D analouge of the Lazy Caterers' Sequence is called the Cake number.

Using n as 100 in the given formula we get 166751 as the answer.

When cut by 4 planes When cut by 4 planes

Formula : Formula : ( Image and Animation Source: Wikipedia )

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Also, you may write the answer as:

( n 0 ) \large {n \choose 0 } + ( n 1 ) \large {n \choose 1 } + ( n 2 ) \large {n \choose 2} + ( n 3 ) \large { n \choose 3 }

Ossama Ismail - 4 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...