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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 Calculator 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)