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

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<stdio.h>
    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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