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# The formula for a pyramid is a little confusing to me, but we're supposed to use it to solve this..?

Ok, I have 5 spheres located on a x,y,z plane. The center of sphere one is as <-1, 1, -1>, the center of sphere two is <1, 1, -1>, the center of sphere three is <-1, 1, 1>, and the center of the fourth sphere is <1, 1, 1>. Each sphere has a radius of 1. The fifth sphere is to be placed on top of the other four so it touches each of the other spheres only once. Where is the center of the fifth sphere?

### 1 Answer

- Anonymous1 decade agoFavorite Answer
The four original points make a square that's parallel to the xy plane. The center point of this square is (0,1,0), which lies right on the y-axis. There are two places you could put the fifth sphere: either behind the square (so that it's closer to the origin) or in front of it. So there are actually two different answers.

Regardless, the center of the sphere is on the y-axis too. This means its x-coordinate is 0 and its x-coordinate is 0. Let's call the center point of the fifth sphere (0, y, 0) for an unknown "y" value.

Since the fifth sphere touches the other four, there's a straight line between the fifth sphere's center point and, for example, the center point of the (1,1,1) sphere. This is a distance of 2. So the distance formula says:

√[(1-0)^2 + (y-1)^2 + (1-0)^2] = 2

Solve this to get two different values for y.