Lesson video

Hello, my name is Mr Chan and in this lesson, we're going to learn how to find the volume of a frustum.

What is a frustum? Well, let's look at the definition of what a frustum is.

A frustum is the portion of a cone or pyramid which remains after its upper part has been cut off by a plane parallel to its base.

So, realistically if you imagine a cone or a pyramid, if you cut off the upper part, what remains is a frustum.

We have a frustum that used to be cone there.

And similary with a pyramid if you cut off this upper part, what remains at the bottom would be a frustum Here is an example of how we would work out the volume of a frustum.

We got a frustum illustrated there in the diagram, now it would make sense that if work out the volume of the large cone, even though we can't see the apart of that there.

We are told that the height of the large cone, is ten centimetres.

We could work out the volume given the formula that is displayed on the screen there.

The radius of the large cone is five centimetres, we can substitute those values into the formula for the volume.

The volume formula is 1/3 pie r squared h.

We are going to use the radius of five centimetres and the height ten centimetres, substitute those values in and simplify that expression to get volume of the large cone which equal 250 pie over three centimetres cubed.

Now, remember the frustum has had the upper the upper part of the cone removed.

The upper part of the cone is a cone again and is a smaller cone this time.

Now, the smaller cone has a radius of three centimetres and also we need to know the height of the smaller cone but that would be the difference between the ten centimetre and the four centimetre of the frustum there.

The height of the smaller cone would be six centimetres.

Let's substitute those values of three radius and six centimetre height into the formula.

We get the volume calculation like this and let's simplify that expression, we get the volume of the smaller cone to be 54 pie over three centimetres cubed.

Now, we can figure out the volume of a frustum now just by subtracting the smaller cone volume from the larger cone, like this.

Once we do work out all that calculation equals.

we get a final answer for the volume of the frustum to be 196 pie over three centimetres cubed.

Here is a question for you to try.

Pause the video to complete the task, resume the video once you are finished.

Here is the answer for question one.

You are given the volume of a cone formula in the previous example.

Make sure you are using the correct radius and the correct height for your twos cone values.

The larger cone has a height of ten centimetres in this question and the smaller cone has a height of six centimetres in this question.

Here is another question you could try.

Pause the video to complete the task, resume the video once you are finished.

Here is the answer.

This question just be careful that you're halving the diameters that you've been given to use the radius and again, you haven't been given the height of the large cone so you going to have to add those two perpendicular heights together.

Just to remind you before you begin this question, That the volume of the pyramid is the base area, multiplied by perpendicular height and divided by three.

Pause the video to a go at this one and resume the video once you are finished.

Here is the answer for this question.

In this question it tell you its a square based pyramid, so that's where you would start off by realising its a square and finding the area of that square base by multiplying two of the sides.

Remember a square has four equal sides.

That's all we have time for this lesson.

Thanks for watching.