Video: Finding the Volume of a Three-Dimensional Composite Figure

Calculate the volume of the figure.

01:54

Video Transcript

Calculate the volume of the figure.

Here, in this figure, essentially, we almost have a full prism — looks like a box — except there’s a piece missing out of the corner. There are two ways that we can find the volume of this figure. We could either find the volume as if it were an entire box in and then take away the missing corner piece or we could cut the figure into pieces and then add the volume of the pieces together.

Let’s solve this both ways. The area of a prism is length times width times height. Here, we can see looking at this as if it were an entire box, the height will be eight, the width will be four, and the length will be nine plus three. So it will be 12. So this would be how to find the volume of the box.

Now, to find that volume of the corner piece that was taken out, it will be the same formula. The width is still four, the length will be three, and the height we’ll have to find. The height will be eight minus six. So it will be two. So the volume of this corner piece will be four times three times two. So we get 384 minus 24. Therefore, the volume would be 360 centimetres cubed.

So now, let’s look at this if we were adding pieces together, we would have the blue piece and then the black piece. So we need to find the volume of each piece and add them together. So let’s begin with the blue. The height is six, the length is three, and the width is four.

And now for the volume of the black piece. The length will be nine, the width will be four, and then the height will be eight. So we need to multiply and then add. So we have 72 plus 288, which just as before gives us an answer of 360 centimetres cubed. Therefore, the volume of this figure will be 360 cubic centimetres.

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