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