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Heres the question:

------------------------------------------------------------------------------------------------------------------------------

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.

------------------------------------------------------------------------------------------------------------------------------

I got 1764mm3 but when I went to check my answer it said that I was wrong.

plz help.

Guest Apr 3, 2017
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5+0 Answers

 #1
avatar+4172 
+2

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

hectictar  Apr 4, 2017
 #2
avatar
0

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!blush​​blush​​blush​​blush​​blush​​blush​​blush​​

Guest Apr 4, 2017
 #3
avatar
+1

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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

Guest Apr 4, 2017
 #5
avatar+4172 
+2

Holy cow! That is a loooooooooong link... surprise  Lol !!

hectictar  Apr 4, 2017
 #4
avatar+4172 
+3

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! smileysmileysmiley

hectictar  Apr 4, 2017
edited by hectictar  Apr 4, 2017

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