Work out the volume of the composite prism shown.
It’s called a composite prism because they are prisms put together to make a shape. Here it looks like an H, a 3D H, as in three-dimensional.
So before we begin finding the volume, let’s make sure we know all of the lengths. Notice the little markings shown here. This means they’re all equal. So since one of them is three, they’re all three. Let’s go ahead and split this up into three different prisms.
We will have the green prism in the middle and two white prisms on the outside. And these white prisms are congruent. Here’s how we know. If this length is seven and each of these are three, so three plus three is six, so how much would that leave for this little piece?
Well, six plus what gives us seven? One. And if it’s one on the left-hand side of the middle prism, it must be one over here as well. So that makes this side equal to three plus one plus three, which is seven. And then we also have this four, the depth. Well if this is four, the depth of the green prism also must be the exact same.
So it would be four, making this side four and making this side four. So there a lot of numbers here. Let’s just separate them and take it step by step. Let’s find the volume of this prism first. Then we will find the volume of the green prism. And then we’ll find the volume of the white prism and then add them together.
And the volume of a prism formula will be the length times the width times the height of the prism. So for the black prism, that will be seven times one times four. And it wouldn’t matter the order of the length, the width, and height that we put them in because we’re multiplying.
And it won’t matter because we’re multiplying them all together no matter what. And we get 28. For the green prism, we have one times two times four to give us eight. Let’s make the white prism pink, that way we can use that color. It would be a little difficult to write in white.
So the length, the width, and the height of the pink prism will be seven times one times four to give us 28. So that should make sense. It’s the exact same volume as the black prism. We said that they were identical and we explained why.
So in order to find the volume of this composite prism, we need to take 28 plus eight plus 28, resulting in 64. However, since it’s a volume, we need to add units cubed. So the volume of the composite prism shown would be 64 cubic units.