Sphere Formula

Sphere is a solid 3 dimensional (x-axis, y-axis, and z-axis), geometrical shape, symmetrical circular-shaped object. It does not have any flat surfaces, edges, and vertices. Sphere examples are football, Basket Ball, World Globe, Plants, and more.

Characteristics of a Sphere

A list of Characteristics of a Sphere is given below –

A sphere is a three-dimensional solid symmetrical object.
It is round in shape.
Based on its radius, it has a surface area and volume.
It does not have any corners, edges, and faces.

Component of Sphere

A Sphere contains the following components –

Diameter – The longest line that passes through the center of a Sphere is called Diameter. It is denoted by D or d.

Radius – Half of a Diameter is called radius. It is denoted by R or r.

Formulas of a Sphere

The below table shows the three main formulas of a Sphere –

Diameter of a Sphere	D=2r
Surface Area of a Sphere	A=4πr²
Volume of a Sphere	V=(4⁄3)πr³

Where, r=radius of a Sphere

π =22⁄7 or 3.14

D = Diameter of a Sphere

A = Area of a Sphere

V = Volume of a Sphere

Example 1:

If the radius of a sphere is 5 cm, then calculate the following:

Diameter of a Sphere
Surface area of a Sphere
Volume of a Sphere

Solution:

Given –

Radius of a Sphere (r) = 5 cm

(i) Diameter of a Sphere (D) = 2r

= 2×5 = 10 cm

(ii) Surface area of Sphere (A) = 4πr²

= 4×3.14×5×5 = 314 cm²

(iii) Volume of a Sphere (V) = (4⁄3)πr³

Sphere Formula

Example 2: Write a C program to calculate the following –

Diameter of a Sphere
Surface area of a Sphere
Volume of a Sphere

Code:

  #include      void main()      {         int d,r;         float pie = 3.14;         double a, v;         printf(“Enter radius of a Sphere”);         scanf(“%d”, &r);          d = 2*r; // formula to calculate diameter of a Sphere          a = 4*pie*(r*r); // formula to calulate Area of a Sphere          v = (4.0/3.0)*pie*(r*r*r); // formula to calculate Volume of a Sphere          printf(“Diameter of a Sphere is = %d”, d);          printf(“n”);          printf(“Area of a Sphere is = %f”, a);          printf(“n”);          printf(“Volume of a Sphere is = %f”, v);      }  

Output:

Enter radius of a Sphere 5  Diameter of a Sphere is = 10  Area of a Sphere is = 314.000000  Volume of a Sphere is = 523.333351

Example 2: Write C++ program to calculate Sphere Formulas –

Code:

  #include<iostream>  using namespace std;  int main()  {  int radius,vol,dia,area;  cout<<“Enter Radius of Sphere : “;  cin>>radius;  dia = 2*radius;  area = 4*3.14*(radius*radius);  vol = (4*3.14*radius*radius*radius)/3;  cout << “Diameter of Sphere = “<<dia;  cout << “n”;  cout << “Area of Sphere = “<<area;  cout <<“n”;  cout << “Volume of Sphere = “<<vol;  return 0;  }  

Output:

Enter Radius of Sphere : 9  Diameter of Sphere = 18  Area of Sphere = 1017  Volume of Sphere = 3052

Example 3: Write a Java Program to calculate diameter, area, and volume of a Sphere.

Code:

  public class MyClass  {        public static void main(String args[])        {        int radius = 7;        double pie = 3.14285714286;       int diameter = 2*radius; // calculate Sphere Diameter      double area = 4*pie*(radius*radius); // Calculate Sphere area       double volume = (4.0/3.0)*pie*(radius*radius*radius);  // Calculate Sphere Volume      //ptint value of Diameter, Area, and Volume of a Sphere      System.out.println(“Diameter of Sphere = ” +diameter);      System.out.println(“n”);      System.out.println(“Area of Sphere = ” + area);      System.out.println(“n”);      System.out.println(“Volume of the sphere = ” +volume);         }    }  

Output:

Diameter of a Sphere = 14  Area of a Sphere = 616.000000  Volume of a Sphere = 1437.33333333464

Example 4: Write a PHP program to calculate following Sphere formulas –

Diameter of a Sphere
Surface area of a Sphere
Volume of a Sphere

Code:

  <html>  <head>  <title>Sphere Formulas</title>  <body>  <?php          $radius = 18;        $pie = 3.14285714286;    $diameter= 2*$radius; /* to calulate sphere diameter */  $area= 4*$pie*($radius*$radius); /* to calculare Sphere area */      $volume=(4/3)*$pie*($radius*$radius*$radius); /* to calculate Sphere Volume */  echo “Diameter of the Sphere = “;  echo $diameter;      echo “<br>”;  echo “Area of the Sphere = “;  echo $area;      echo “<br>”;      echo “Volume of the Sphere = “;        echo $volume;         ?>     </body>  </head>  </html>  

Output:

Diameter of the Sphere = 36  Area of the Sphere = 4073.1428571466  Volume of the Sphere = 24438.857142879

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