Heres the question:
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The solids are similar. Find the volume of the red solid.
The picture isn't working so heres what it looks like:
The blue solid has a square base. Both sides of this base are 21mm long and it says the volume is 5292
The red solid also has a square base. Both sides of this base are 7mm long.
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I got 1764mm3 but when I went to check my answer it said that I was wrong.
plz help.
I think this is what the picture probably looks like:
Since the boxes are similar, I knew that the height of the red box was h/3.
volume = length * width * height
5292 cubic mm = 21 * 21 * h
Solve for h:
h = 5292 / 441 = 12 mm
red box volume = 7 * 7 * (12/3)
red box volume = 196 cubic mm
Also,
since you are reducing 3 dimensions by 3,
the new volume = old volume / 33
the new volume= 5292 / 27 = 196 cubic mm
O yeah. So sorry. I forgot to mention this and it is going to be really stupid but they are square pyramids, should've mentioned that. Sorry again!
okay. this is going to sound even more stupid.
So I go to the question and put in your answer just for grins even though they are clearly square pyramids, check your answer, and it's right!
There must have been a glitch.
btw here's the image's link: data:image/png;base64,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
Oh no! Haha okay in that case, this is probably what the picture looks like:
volume = (1/3)(area of base)(height)
5,292 = (1/3)(21)(21)(h)
h = 5,292 / 147 = 36 mm
red volume = (1/3)(7)(7)(36/3)
red volume = 196 cubic mm
As you can see, it is the same answer either way.
Because you are reducing 3 dimensions by 3, the volume will reduce by 3, 3 times.
The new volume = old volume / 33
5,292 / 33 = 196
That is all the math you really need to do.
It wasn't really necessary to go through all that work that I showed.
It isn't a glitch!