# Solving the Equation of a Sphere with Diameter Endpoints

• mamma_mia66
In summary, the equation of the sphere with a diameter whose endpoints are at (-1,1,-3) and (3,-1,2) is (x-1)^2 + y^2 + (z+1/2)^2 = 21/4. The center of the sphere is (1,0,-1/2) and the radius is 5.25.
mamma_mia66

## Homework Statement

Write the equation of the sphere whose diameter has endpoints at (-1,1,-3) and (3,-1,2).

## The Attempt at a Solution

(x-x1)2+ (y-y1)2+ (z-z1)2= r2

the center of the sphere is : (1,0,-1/2)
r= $$\sqrt{}5/4$$

then the equation is: (x-1)2+(y-0)2+(z+1/2)2=5/4

Please someone check my answer and if I am not right, help me to solve it.

mamma_mia66 said:
the center of the sphere is : (1,0,-1/2)
r= $$\sqrt{}5/4$$

Hi mamma_mia66!

Centre is right.

But r is wrong.

(you've calculated the distance from the centre to the origin! )

I am not sure that I know how to find the r ? too old to remember it after so many years not being in school.

Yes you do!

they've given you a diameter

r= sq. rt. (3-1)2+ (1-0)2+(2-1/2)2= 21/4

Last edited:

## 1. How do I find the equation of a sphere given its diameter endpoints?

To find the equation of a sphere, you will need to know the coordinates of the two endpoints of its diameter. Let's call these points (x1, y1, z1) and (x2, y2, z2). The equation of a sphere with these endpoints is (x - x1)^2 + (y - y1)^2 + (z - z1)^2 = (x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2.

## 2. What does the equation of a sphere represent?

The equation of a sphere represents all the points in 3D space that are equidistant from a given center point. In simpler terms, it represents the surface of a 3D ball with a specific radius and center point.

## 3. Can I use the equation of a sphere to find the volume and surface area?

Yes, you can use the equation of a sphere to find its volume and surface area. The volume can be calculated using the formula V = (4/3)πr3, where r is the radius of the sphere. The surface area can be calculated using the formula A = 4πr2.

## 4. Is there a way to graph the equation of a sphere?

Yes, you can graph the equation of a sphere by plugging in different values for x, y, and z and plotting the resulting points on a 3D graph. This will give you a visual representation of the sphere in 3D space.

## 5. Are there any real-life applications of the equation of a sphere?

The equation of a sphere has many real-life applications, including in fields such as engineering, architecture, and physics. It is used to calculate the volumes and surface areas of objects with spherical shapes, as well as in the design of curved structures such as domes and lenses.

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