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A solid metal cuboid whose dimensions are two 𝑥 centimeters, six 𝑥 centimeters, and 10𝑥 centimeters was melted and made into small cubes.
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If the edges of the small cubes are two 𝑥 centimeters, how many can be made from the melted cuboid?
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So, what we’re gonna do is look at the cuboid and cubes separately.
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So first of all, what we want to do is find out the volume of each of them.
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Well, the volume of a cuboid is equal to the length multiplied by the width multiplied by the height.
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And the volume of a cube is equal to the length cubed, and that’s because all of the lengths are the same.
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But if we take a look at the cuboid, dimensions are two 𝑥, six 𝑥, and 10𝑥.
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So therefore, the volume is gonna be these dimensions all multiplied together, so two 𝑥 multiplied by six 𝑥 multiplied by 10𝑥.
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So what this is gonna give is 120𝑥 cubed.
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And that’s because two multiplied by six is 12 multiplied by 10 is 120.
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Then 𝑥 multiplied by 𝑥 multiplied by 𝑥 is 𝑥 cubed.
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And the units for this would be centimeters cubed.
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And now if we move on to the cube, the volume of the cube is equal to two 𝑥 cubed.
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And then this again will give us eight 𝑥 cubed.
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And then once again, the units would be centimeters cubed.
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But we don’t need to really use them at the moment because we don’t need them for this step.
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Well, it’s worth noting here that the answer was eight 𝑥 cubed for the volume.
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But be careful.
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A common mistake is to put two 𝑥 cubed.
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And that’s because students forget to cube the two as well as the 𝑥.
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Okay, so now we know the volume of the cuboid and the volume of the cube.
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What is the next step to solving this problem?
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Well, what we want to do now is work out the number of cubes that could be made from the melted cuboid.
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So to do that, what we’re gonna do is divide the volume of the cuboid by the volume of the cube.
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So we’ve got 120𝑥 cubed over eight 𝑥 cubed.
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Well, first of all, we can see that we got 𝑥 cubed in the numerator and denominator, so we can divide through by 𝑥 cubed.
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Well, what this leaves us with is 120 over eight.
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Well, 120 divided by eight is 15.
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So therefore, we can say that 15 cubes could be made from the melted cuboid.