# Frustums

A frustum is the shape you are left with if you cut the top part (the pointy bit) of a cone or pyramid off parallel to its base.

To remember this picture the following:

Wow was she **frustrated** (frustum) she lost the whole of the **top** of her ice cream **cone**. (The frustum is the bit that fell on the floor).

**Example**

The first diagram shows a cone of base radius 12 cm and perpendicular height 10 cm. A small cone of base radius 6 cm and perpendicular height 5 cm is cut off the bottom to leave a frustum. The frustum has a lower radius of 6 cm, an upper radius of 12 cm and a perpendicular height of 5 cm (see second diagram).

Find the volume of the frustum, giving your answer in terms of `pi`.

**Answer:**

`Volume\ of\f\rustum=1/3piR^2H-1/3pir^2h`

`Volume\ of\f\rustum=(1/3pi12^2\times10)-(1/3pi6^2\times5)`

`Volume\ of\f\rustum=(1/3pi144\times10)-(1/3pi36\times5)`

`Volume\ of\f\rustum=(1/3pi\times1440)-(1/3pi\times180)`

`Volume\ of\f\rustum=(480pi)-(60pi)`

`Volume\ of\f\rustum=420pi`

**Answer: **

`420picm^3`