C Program to find Volume and Surface Area of a Cone

How to write C Program to find Volume and Surface Area of a Cone with example?. Before we step into the C Program to find Volume and Surface Area of a Cone, Let see the definitions and formulas behind the Surface area of a Cone and Volume of a Cone.

C Surface Area of a Cone

If we know the radius and Slant of a Cone, we calculate the Surface Area of Cone using the below formula:

  • Surface Area = Area of the Cone + Area of Circle
  • Surface Area = πrl + πr²

Where r= radius and l = Slant (Length of an edge from the top of the cone to edge of a cone)

If we know the radius and height of a Cone, we calculate the Surface Area of Cone using the below formula:

  • Surface Area = πr² +πr √h² + r²

We can also write it as  Surface Area = πr (r+√h² + r²)
Because radius, height, and Slant make the shape as right-angled Triangle. So, Using the Pythagoras theorem:

  • l² = h² + r²
  • l = √h² + r²

The Volume of a Cone

The amount of space inside the Cone called Volume. If we know the radius and height of the Cone then we can calculate the volume using the formula:

  • Volume = 1/3 πr²h (where h= height of a Cone)
  • The Lateral Surface Area of a Cone = πrl

C Program to find Volume and Surface Area of a Cone

This C program allows the user to enter the value of a radius and height of a cone. Using these values, this C program will calculate the Surface Area, Volume, length of a side (Slant), and Lateral Surface Area of a Cone as per the formulas.

/* C Program to find Volume and Surface Area of a Cone */
#include <stdio.h>
#include <stdio.h>

int main()
{
  float radius, height;
  float Volume, SA, l, LSA;
  
  printf("\n Please Enter Radius and Height of a Cone\n");
  scanf("%f %f", &radius, &height);

  l = sqrt(radius * radius + height * height);
  SA = M_PI * radius * (radius + l);
  Volume = (1.0/3) * M_PI * radius * radius * height;
  LSA = M_PI * radius * l;

  printf("\n Length of a Side (Slant)of a Cone = %.2f", l);    
  printf("\n Surface Area of a Cone = %.2f", SA);
  printf("\n Volume of a Cone = %.2f", Volume);
  printf("\n Lateral Surface Area of a Cone = %.2f", LSA);

  return 0;
}

C Program to find Volume and Surface Area of a Cone

In this C program to find Volume and Surface Area of a Cone example, We have entered the Radius of a Cone = 5 and Height = 12

As per the Pythagoras theorem, We can calculate the Slant (Length of a side):
l² = h² + r²
l = √h² + r²
l = √12² + 5²
l = √144 + 25
l = √169
l = 13

The surface Area of a Cone is
Surface Area of a Cone = πr² +πrl
Surface Area of a Cone = πr (r + l)
Surface Area of a Cone = M_PI * radius * (radius + l)
Surface Area of a Cone = 3.14 * 5 * ( 5 +13)
Surface Area of a Cone = 3.14 * 5 * 18
Surface Area of a Cone = 282.6

The Volume of a Cone in C Programming is
Volume of a Cone = 1/3 πr²h
Volume of a Cone = (1.0/3) * M_PI * radius * radius * height
Volume of a Cone = (1.0/3) * 3.14 * 5 * 5 * 12;
Volume of a Cone = 314

The Lateral Surface Area of a Cone in C is
Lateral Surface Area = πrl
Lateral Surface Area = M_PI * radius * l
Lateral Surface Area = 3.14 * 5 * 13
Lateral Surface Area = 204.1

Let us calculate the radius of a Cone using the radius without using the Slant (Standard Formula):
Surface Area of a Cone = πr² +πr √h² + r²
Surface Area of a Cone = πr (r + √h² + r²)

Surface Area = M_PI * radius * ( radius + sqrt ( (height * height) + (radius * radius) ) )
Surface Area of a Cone = 3.14 * 5 * ( 5 + √12² + 5²)
Surface Area of a Cone = 3.14 * 5 * ( 5 + √169)
Surface Area of a Cone = 3.14 * 5 * ( 5 + 13)
Surface Area of a Cone = 3.14 * 5 * 18
Surface Area of a Cone = 282.6

About Suresh

Suresh is the founder of TutorialGateway and a freelance software developer. He specialized in Designing and Developing Windows and Web applications. The experience he gained in Programming and BI integration, and reporting tools translates into this blog. You can find him on Facebook or Twitter.