Please help: "The base of the pyramid is a square with a side length of 2√3, and the height of the pyramid is 3cm, with its apex..."
- Thread starter NNikola
- Start date
- Joined
- Feb 4, 2004
- Messages
- 16,583
What formulas or methods have they given you? What are your thoughts? What have you tried? How far have you gotten? ("Read Before Posting")
Please be complete. Thank you!
I've drawn the pyramid and it happens to be oblique. The center of the sphere is not on any meaningful location that would help me calculate the radius and I don't have any idea how to solve this. This is a problem from my highschool prep book and no formulas or hints were given to me. So yeah i have no idea how would I get the sphere radius here.
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,087
What does that mean? It sounds as if the apex is in the plane of the base, which makes no sense. Is it perhaps meant to say that the apex is directly above the center of an edge??
Yes the apex is directly above the center of one sides of the base, not within it. I've drawn a picture above.
I'm not a native english speaker so i translated the text, sorry for misunderstanding.
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,087
I figured that. And the picture is definitely helpful in clarifying when words are difficult!
You do know that the center of the sphere is on the vertical line through the center of the square ABCD, right?
It will also be on the horizontal line through the circumcenter of the vertical triangle ADE containing the apex.
Do these ideas help?
First, we draw a picture of the pyramid with the base ABCD and the top E.
We calculate the distance between two points using Pythagoras' theorem.
The centre of the sphere is the same distance from all five points of the pyramid: dist(M,P) = |MA| = |MB| = ... = r
At the end you get the coordinates of the centre point M(m1 | m2 | m3) and the radius r of the sphere.
What are your approaches and calculations?
Mathematical greetings from Leonie
We calculate the distance between two points using Pythagoras' theorem.
The centre of the sphere is the same distance from all five points of the pyramid: dist(M,P) = |MA| = |MB| = ... = r
At the end you get the coordinates of the centre point M(m1 | m2 | m3) and the radius r of the sphere.
What are your approaches and calculations?
Mathematical greetings from Leonie
Last edited: