# Really Easy Ways to Calculate the Surface Area of a Cone

What is the equation for surface area of a simple or truncated cone? Here, you will find the answers.

Omkar Phatak

Last Updated: Feb 26, 2019

What is a Right Circular Cone?

This type has a circular base and the axis passing through the vertex is perpendicular to the base of the cone. Viewed sideways, it looks like two identical right angled triangles, placed with one of their sides (other than hypotenuse and base), connected back-to-back and their bases aligned in a straight line.

Formula

There are two different components that you need to calculate, while determining the surface area.

Total Surface Area of a Cone = (Area of Circular Base of Cone) + (Area of Curved or Lateral Surface Area of the Cone)

Total Surface Area of a Cone = (Area of Circular Base of Cone) + (Area of Curved or Lateral Surface Area of the Cone)

^{2}, where R is the radius of the base.

^{2}+ H

^{2})

where 'H' is the surface area of the cone.

*Cone Surface Area*= πR^{2}+ πRS = πR (R + S)While calculating, if the slant height (S) is not given, then calculate it using the Pythagorean theorem relation, mentioned earlier.

Volume of a Right Circular Cone

It is useful to know the formula for volume too. The volume of a cone is given by the following formula:

where H is the perpendicular height and R is the radius of circular base. To calculate volume, all you have to do is plug in these known values.

**V**_{Cone}= 1/3 πR^{2}Hwhere H is the perpendicular height and R is the radius of circular base. To calculate volume, all you have to do is plug in these known values.

Truncated Cone or Frustum

A truncated cone or frustum is the geometrical object created, when the top of the cone is cut off, leaving a flat parallel base at top. The surface area and volume of such an object is given by the following formulas:

**where**

*Surface Area of Truncated Cone*= π [(R_{1}^{2}+ R_{2}^{2}) + √{(R_{1}^{2}- R_{2}^{2})^{2}+ (H(R_{1}+ R_{2}))^{2}}]- R
_{1}= Top Base Radius - R
_{2}= Bottom Base Radius - H = Perpendicular Height of Frustum

**where again**

*= πH/3 (R*

Volume of Truncated ConeVolume of Truncated Cone

_{1}^{2}+ R_{2}^{2}+ R_{1}R_{2})- R
_{1}= Top Base Radius - R
_{2}= Bottom Base Radius - H = Perpendicular Height of Frustum