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**Equation of a Sphere Calculator + Online Solver With Free Easy Steps**

The online **Equation of a Sphere Calculator** is an online tool that allows you to calculate the radius and center point of a sphere.

The **Equation of a Sphere Calculator** is a powerful tool that can be used by mathematicians and scientists to efficiently use the sphere’s general equation and find the radius needed for their calculations.

**What Is an Equation of a Sphere Calculator?**

**The Equation of Square Calculator is an online calculator that helps you find a sphere’s radius and center using its general equation.**

The **Equation of a Sphere Calculator **requires a single input to work. The calculator allows you to input the general equation of the sphere along with the x , y, and z values and click the “Submit” button.

**How To Use an Equation of a Sphere Calculator?**

To use the **Equation of a Sphere Calculator**, add the inputs into the calculator and click the “Submit” button.

The detailed instructions on how to use the calculator are given below:

**Step 1**

First, we enter the general equation of the sphere into the **Equation of a Sphere Calculator**.

**Step 2**

Finally, after entering the** Equation of a Sphere Calculator**, we click the **“Submit”** button. The calculator displays the results instantly and gives you the radius and center values of the sphere.

**How Does an Equation of a Sphere Calculator Work?**

The **Equation of a Sphere Calculator** works by taking in the inputs and calculating the radius and the center value between the sphere. The following Equation of a Sphere is used to calculate the radius and center value of the sphere:

** x$^{2}$ + y$^{2}$ + z$^{2}$ = r$^{2}$**

Where:

x, y, z = the coordinates of the sphere.

r = radius of the sphere.

**What Is a Sphere?**

A **sphere **is a round, three-dimensional object that has no vertices or edges, unlike other three-dimensional shapes. Every point on its surface is equidistant from the center. In other words, the distance between the **sphere’s center **and any point on its surface is the same.

A **sphere **is a circular, three-dimensional solid figure in geometry. It comprises a collection of points connected in three dimensions by a single common point at equal distances.

A tennis ball, a basketball, a soap bubble, etc., are some examples of **spheres**. The following are a **sphere’s **main components:

**Radius**

The **radius **is the length of the line segment drawn from any point on the sphere’s surface to its center.

**Circumference**

The **circumference **of a sphere is its length measured along its great circle. The **circumference **of the dotted circle in the illustration below, or the cross-section of the sphere that contains its center, is depicted.

**Surface Area of a Sphere**

The **surface area** of a **sphere **is the space that the sphere’s outer surface occupies. It has a square unit of measurement. The following is the formula to determine the surface area of a sphere:

\[ \text{Surface Area of Sphere} = 4\pi r^{2} \]

**Volume of a Sphere**

The amount of space a sphere can occupy is determined by its **volume**. Cubic units are used to measure it. The following is the **volume **formula for the sphere:

\[ \text{Volume of Sphere} = \frac{4}{3} \pi ^{3} \]

**Solved Example**

The **Equation of a Sphere Calculator **can easily help you find the radius and center of the sphere. Here are some examples solved using the **Equation Sphere Calculator:**

**Example 1**

A high school student needs to find the radius and center of a circle. The student is provided with the following equation:

** x$^{2}$ + y$^{2}$ + z$^{2}$ + x – 2y – 3z – 10 = 0 **

Using the** Equation of a Sphere Calculator,** find the radius and center point of the sphere.

**Solution**

To find a sphere’s radius and center point, we can use the **Equation of a Sphere Calculator**. First, we input the general equation given to us in the **Equation of a Sphere Calculator**; the general equation of the sphere is x$^{2}$ + y$^{2}$ + z$^{2}$ + x – 2y – 3z – 10 = 0.

After entering the general equation into the **Equation of a Sphere Calculator**, we click the **“Submit”** button on the calculator. The calculator instantly displays the results, which are displayed below the calculator.

The following results are extracted from the **Equation of a Sphere Calculator**:

Input Interpretation:

Surface:

\[ \text{Cartesian Equation} : x^{2}+y^{2}+z^{2}+x-2y-3z-10=0 \]

Results:

\[ \text{Radius} = \sqrt[3]{\frac{3}{2}} \approx 3.67423 \]

\[ \text{Center} = \left ( -\frac{1}{2},1,\frac{3}{2} \right ) = (-0.5,1,1.5) \]

**Example 2**

During his assignment, a college student is given a spherical ball’s general equation as follows:

** x$^2$ + y$^2$ + z$^2$ + 5x – 3y – 3z – 4 = 0 **

To complete his assignment, the student must find the ball’s radius and center point. With the help of the **Equation of a Sphere Calculator, **find the ball’s radius and center point.

**Solution**

We can use the **Equation of a Sphere Calculator** to get a sphere’s radius and center point. To begin, we enter the general equation into the **Equation of a Sphere Calculator**; the general equation of the sphere is x$^{2}$ + y$^{2}$ + z$^{2}$ + 5x – 3y – 3z – 4 = 0.

We enter the general equation into the** Equation of a Sphere Calculato**r and press the **“Submit” **button. The calculator displays the results instantaneously, which are presented below the calculator.

The following results are taken from the **Equation of a Sphere Calculator**:

Input Interpretation:

Surface:

\[ \text{Cartesian Equation} : x^{2}+y^{2}+z^{2}+5x-3y-3z-4=0 \]

Results:

\[ \text{Radius} = \text{Radius} = \frac{\sqrt{59}}{2} \approx 3.84057 \]

\[ \text{Center} = \left ( -\frac{5}{2},\frac{3}{2},\frac{3}{2} \right ) = (-2.5,1.5,1.5) \]

**Example 3**

Consider the following equation:

**x$^{2}$ + y$^{2}$ + z$^{2}$ + 2x – 2y – 2z – 2 = 0 **

Use the** Equation of a Sphere Calculator** to find the radius and center of the sphere.

**Solution**

The radius and center of a sphere can be determined using the **Equation of a Sphere Calculator**. We start by entering the sphere’s general equation, which is written as x$^{2}$ +y$^{2}$ +z$^{2}$ + 2x – 2y – 2z – 2 = 0, into the **Equation of a Sphere Calculator**.

The general equation is entered into the **Equation of a Sphere Calculator**, and then we click “Submit.” The calculator immediately displays the findings, which are shown in a table below the calculator.

The calculator results are displayed below:

Input Interpretation:

Surface:

\[ \text{Cartesian Equation} : x^{2} + y^{2} +z^{2}+2x-2y-2z-2=0 \]

Results:

\[ \text{Radius} = \text{Radius} = \sqrt{59} \approx 2.23 \]

**Center = (-1,1,1) **