My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 27th, 2013, 10:43 AM   #1
Newbie
 
Joined: Mar 2013

Posts: 2
Thanks: 0

Area of sphere inside cube

Ok, so a cube and a sphere are both centered at origo. The cube has side lengths L. I need to know the surface area of the part of the sphere that is inside the cube, for all possible r. There will be three different equations, one for , when the entire sphere is inside the cube, one for , when six spherical caps of the sphere stick out of the cube sides , and one for , when only the corners of the cube is visible. I have figured out the two first, but not the last.

Any help would be greatly appreciated!
morjo is offline  
 
March 27th, 2013, 12:41 PM   #2
Senior Member
 
Joined: Feb 2012

Posts: 628
Thanks: 1

Re: Area of sphere inside cube

Calculate the cross-sectional area for the smaller part of the sphere cut by the plane which coincides with one of the sides of the cube, and call this area C.

Now, imagine six of these cross-sectional areas, one for each side of the cube. Let the area divided by two adjacent cross-sections along an edge be E, the area within any one cross-section not shared by the others F, and the area of the sphere not covered by these cross-sections be X. Now, we want to calculate X, since the area of the sphere not covered by these cross-sections is the area of the sphere which is inside the cube. Letting A represent the surface area of the whole sphere, we have the following equations:

6C = 24E + 6F (since there are 6 faces and 12 edges but each edge section is counted twice)

A = 6F + 12E + X

6C - A = 12E - X

Now, if you can calculate E, then you can calculate X. I don't know how hard it would be to calculate E though.
icemanfan is offline  
March 27th, 2013, 02:09 PM   #3
Newbie
 
Joined: Mar 2013

Posts: 2
Thanks: 0

Re: Area of sphere inside cube

Quote:
Originally Posted by icemanfan
Now, if you can calculate E, then you can calculate X. I don't know how hard it would be to calculate E though.
This is a good start, thanks E is kind of like a spherical lune, except it is an intersection between the sphere and two SMALL circles, not two large. The two small circles are perpendicular to each other. It could be calculated as 2 times the area of the sphere bounded by one great circle and one small, the small having a distance L/2 from the center and a 45 degree angle to the great circle. Anyone know how to calculate such an area?
morjo is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
area, cube, inside, sphere



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
A cube is inscribed inside a sphere abowlofrice Algebra 8 March 3rd, 2019 01:16 AM
Surface area of sphere caters Algebra 5 January 1st, 2014 01:34 AM
Largest square inside a cube proglote Algebra 16 June 11th, 2011 03:50 PM
Surface Area of Sphere Recipe Calculus 5 January 12th, 2010 04:07 PM
sphere volume surface area kapital Elementary Math 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.