In this article we will show you, How to write C Program to find Volume and Surface Area of a Cone with example. Before we step into the program, Let see the definitions and formulas behind 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 then 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 top of the cone to edge of a cone)

If we know the radius and height of a Cone then 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 Pythagorus theorem:

- l² = h² + r²
- l = √h² + r²

### Volume of a Cone

The amount of space inside the Cone is called as 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 user to enter the value of a radius and height of a Cone. Using these values it 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**

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 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 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

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