# 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 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;
}```

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