Finding the area of cross section

[Rachiesweet14]

Hi Im am not sure how to find the area of cross sections. One particular problem had me confused. Here it is,

A sphere w/ radius 5 is cut by a plane 3cm from the top. Find the area of the resulting cross section. The following picture is the one i drew. My answer was "By geometric mean the radius is 3 times two which equals 6 and than i took the square root of six. I then concluded that the area of the cross section is Pi times the square root of 6 squared which equals 6 pi or 18.84955592.
Please someone help me i really need to learn this.
thanks

 

[tkhunny]

Have you considered the Pythagorean Theorem?

\(\displaystyle Radius^{2} + 2^{2} = 5^{2}\)

 

[Rachiesweet14]

?

Have you considered the Pythagorean Theorem?

\(\displaystyle Radius^{2} + 2^{2} = 5^{2}\)

I dont understand what you are saying. Do you mind drawing a visual representation?

 

[Rachiesweet14]

Google "spherical cap"; you'll get plenty of sites, like:
http://en.wikipedia.org/wiki/Spherical_cap

Thank you very much