Chapters

## Circle Definition

**break them down**into simple two dimensional shapes.

A | B |

Pyramid | Can be broken down into four triangles and a square |

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

A | The radius goes from the centre point to the edge of the circle. |

B | The diameter goes from end to end of the circle, passing through the centre point. |

C | The circumference is the length around the circle, or the perimeter |

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.

A | B |

Cylinder | Can be broken down into a rectangle and a circle |

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.

Definition | When it’s used | |

Surface Area | The area of the ‘surface’ of the shapes that make up a three dimensional object | For three dimensional shapes |

## 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.

Rectangle | A = l*w |

Rectangle of a cylinder | A = l*h |

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

**length**around the circle, known as the circumference.

Rectangle | A = l*w |

Rectangle of a cylinder | A = C*w |

**surface**area 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.**

A | B |

Cone | Can be broken down into a circle and a ice cream cone shape |

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.**

l | The length of the slant height of the cone |

r | The radius of the circle |

h | The height from the centre point of the circle to the apex |

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.

Definition | |

Truncated | To truncate is to shorten. If something is truncated, it means that it has been shortened or cut. |

Truncated Cone | A cone that is cut by a plane parallel to its base. |

A | B |

Truncated Cone | Can be broken down into two circles and a ice cream cone shape |

## 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.

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