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.

## 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; }

**OUTPUT**

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 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