# Equation of a Sphere Calculator

Equation of a Sphere calculator is used to calculate the radius and centre point of a sphere Mathematicians and scientists can use the Equation of a Sphere Calculator to apply the sphere's general equation effectively and determine the radius required for their computations.

## What Is a Sphere?

Contrary to other three-dimensional shapes, a sphere is a circular, three-dimensional solid shape without vertices or edges. It comprises a group of points connected in three dimensions at equal distances by a single common point. The distance between each point on its surface and the centre is similar.

## Surface Area of a Sphere

The area that a sphere’s exterior surface takes up is known as surface area. Its unit of measurement is the square. We can use the following equation to calculate a sphere’s surface area:

$$4 π r^2$$ square units

## Volume of a Sphere

The volume of a sphere determines how much space it can fill. It is measured in cubic units. The volume formula for the sphere is as follows:

$$\dfrac{4}{3} π r^3$$ cubic units

## Equation of a Sphere Example

Example 1: When the sphere’s centre and radius are provided as (11, 8, -5) and 5 cm, respectively, write the sphere equation in standard form.

Given: Centre = (12, 9, -6) = (a, b, c)

We know that equation of the sphere is:

$$(x – a)^2 + (y – b)^2 + (z – c)^2 = r^2$$

Now, substitute the given values in the above form, and we get:

$$(x – 12)^2 + (y – 9)^2 + (z – (-6))^2 =52$$

$$(x – 12)^2 + (y – 9)^2 + (z + 6)^2 = 25$$

Thus, the equation of the sphere is $$(x – 12)^2 + (y – 9)^2 + (z + 6)^2 = 25$$

## FAQs

What is the centre of a sphere?

A sphere is a three-dimensional object of all points equally spaced out from the centre, a fixed point. A line segment whose endpoints are on the sphere and which goes through the object’s centre is said to have that object’s diameter.

What is the example of a sphere?

Each point on the sphere’s surface is equally spaced from the centre. As a result, the sphere’s centre and surface are always the same distance apart. The radius of the sphere is the name given to this distance. The planets, a ball, and a globe are all examples of spheres.