Question 99330
When trying to find volume for a particular shape you need to know the right formula. In this problem you are trying to find the volume of a cone shape. So the formula for finding the volume of a cone is equal to 1/3 times the area of the base times the height of the cone. The area of a cone is a circle, and the area of a circle is equal to {{{(pi)(r^2)}}}. So the formula for volume of a cone looks like this:
{{{V=(1/3)(pi)(r^2)(h)}}} 
So V is volume
h is the height of the cone
and {{{(pi)(r^2)}}} is the area of the base of the cone (area of a circle)
Ok so lets start with the area of the base part of the formula.
So just deal with the {{{(pi)(r^2)}}} part for now. We are given the diameter is 420mm. First we need to convert that into the radius. Well the radius of a circle is always 1/2 the diameter. So just divide 420 by 2. That would make the radius 210mm. Now just use 210 for r in the area formula {{{(pi)(r^2)}}} so using a calculator that has a {{{(pi)}}} key I got 138544.236
If you use 3.14 for {{{(pi)}}} you should get 138474.
Using a calculator with a {{{(pi)}}} key is more accurate than using just 3.14. The question provided doesn't say what it wants you to use for {{{(pi)}}} so you will have to ask your instructor what they want. 
Anyways now it is just a matter of pluging in the values you have into the volume formula. The height is given as 480mm so your equation should look like this:
{{{V=(1/3)(138544.236)(480)}}}   or    {{{V=(1/3)(138474)(480)}}}
Depending on which value of {{{(pi)}}} use to find the area of the base.

So using the caculator I got V= 22167077.76 cubic mm
using 3.14 I got V = 22155840 cubic mm

Again the difference is because of the value used for {{{(pi)}}}. The instructor or question should specify what to use. If in doubt always use a calculator with a {{{(pi)}}} function.