Truncated Cone

The base of a cone is simply a circle. Let’s take a look at the characteristics that define circles.

Let’s take a look at the formula for the area of any circle.

	Formula
Area

Cylinder

Now that you know the properties of a circle, let’s take a look at what a cylinder is. A cylinder is an easier three dimensional shape to understand than a cone. This is because it can be broken down into simple shapes.

As you can see, a cylinder is nothing more than a base of a circle and a body of a rectangle. We can easily find the area of these two shapes. When we add up the area of these two, we get a special type of area called a surface area.

Surface Area of a Cylinder

In order to find the surface area of a cylinder, we simply need to take the sum of the area of the circle at its base and the rectangle that forms its body. Let’s recall the formula for the area of a rectangle.

When you have the rectangle of a cylinder, the width of the cylinder is simply the height of the cylinder.

Rectangle Area	Area of Two Circles	Surface Area
C*h =	2C =

Cone Definition

Now, let’s take a look at a cone. A cone is a three dimensional shape that also has a base of a circle. However, instead of having the body of a rectangle, it has the body of an ice cream cone.

While it might seem like an unusual shape, we encounter cones in daily life all the time. A cone has what is called a base, which is the bottom, and an apex, which is the top point of the cone.

Surface Area of a Cone

The surface area of a cone can be found with the following formula.

	Formula
Cone Surface Area

Let’s take a look at what these mean.

We get the surface area by simply adding the area of the circle to the area of the cone shape.

Lateral Area of a Cone

In order to understand what the lateral area is, you should first know what it is. The lateral area of the cone is simply the part of the cone that is shaped like a cone or triangle.

A	Lateral Area	A =
B	Circle Area	A =

The lateral area is simply pi times the radius and height.

Volume of a Cone

The volume of a cone can be found with the following formula.

	Formula
Cone Volume

As you can see, the volume of the cone is simply ⅓ times the lateral area of the cone. The volume of any shape is the quantity that a three dimensional shape can hold. While the surface area is simply the total area on the surface of an object, the volume is all the space inside of the object.

Truncated Cone

In order to understand what a truncated cone is, you should know the definition of truncate, or truncated.

Formulas for a Truncated Cone

In order to find the volume and surface areas of a truncated cone, we simply need to follow the formulas below.

Truncated Cone	Formula
Lateral Area
Surface Area
Volume

Keep in mind that R is the radius of the bigger circle and r is the radius of the smaller one.