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# Math : 3-D Geometries

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Re: Math : 3-D Geometries [#permalink]
Wow.. amazing stuff. +1
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Re: Math : 3-D Geometries [#permalink]
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WOOOOOOOOOOOOOOOOOOOOOOOOOOOOOWWWWWWWWWWWWWWWWWWWW

I sense Bunuel has competition!
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Re: Math : 3-D Geometries [#permalink]
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Mathematica be the shizzles.
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Re: Math : 3-D Geometries [#permalink]
Thank you very much!
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Re: Math : 3-D Geometries [#permalink]
Kudos! for writing that up. 3-D is what was missing in GMAT Math Book, gotta update it in compiled GMAT Math Book pdf.
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Re: Math : 3-D Geometries [#permalink]
Thnks for sharing....
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Re: Math : 3-D Geometries [#permalink]
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Thanks a tons for this wonderful post.

This question/ configuration is quite popular(already explained by you in other threads), you might include it as well.
Inscribed Sphere touching the edges of cube.
Cube edge length=a; Radius of sphere=a/2; diagnoal of cube =(3^1/2)*a
The shortest length from edge of the cube to sphere's surface is given by
half the diagnol of cubeminus the raduis of sphere.

[(3^1/2)*a]/2-a/2 =a/2*[(3^1/2)-1]
Attachments

sphere.png [ 19.43 KiB | Viewed 72467 times ]

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Re: Math : 3-D Geometries [#permalink]
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Bumping for review*.

*New project from GMAT Club!!! Check HERE

All Theory Topics: search.php?search_id=tag&tag_id=351
MATH BOOK: gmat-math-book-87417.html
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Re: Math : 3-D Geometries [#permalink]
m]r = (\frac{3V}{4\pi})^{\frac{1}{3}} = (\frac{3 * 972 * \pi}{4 * \pi})^{\frac{1}{3}} = (3*243)^{1/3} = (3^6)^{1/3} = 9[/m]

How exactly did you get from (\frac{3 * 972 * \pi}{4 * \pi})^{\frac{1}{3}} to this ---> = (3*243)^{1/3}

Do we have to multiply the 3 and 972 inside the parntheses? and what happens to the 4?

Thanks
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Re: Math : 3-D Geometries [#permalink]
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sagnik2422
m]r = (\frac{3V}{4\pi})^{\frac{1}{3}} = (\frac{3 * 972 * \pi}{4 * \pi})^{\frac{1}{3}} = (3*243)^{1/3} = (3^6)^{1/3} = 9[/m]

How exactly did you get from (\frac{3 * 972 * \pi}{4 * \pi})^{\frac{1}{3}} to this ---> = (3*243)^{1/3}

Do we have to multiply the 3 and 972 inside the parntheses? and what happens to the 4?

Thanks

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Re: Math : 3-D Geometries [#permalink]
A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64

Solution : Notice that the new cubes will be each of side 1Cm. So on any face of the old cube there will be 5x5=25 of the smaller cubes. Of these, any smaller cube on the edge of the face will have 2 faces painted (one for every face shared with the bigger cube). The number of cubes that have exacly one face painted are all except the ones on the edges. Number on the edges are 16, so 9 per face.

There are 6 faces, hence 6*9=54 smaller cubes with just one face painted.

QUESTION : Number on the edges are 16, so 9 per face.

HOW DO WE KNOW THERE ARE 16 EDGES ? AND FROM THIS HOW IS 9 CALCULATED ?

THANKS
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Re: Math : 3-D Geometries [#permalink]
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sagnik2422
A cube of side 5cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

A. 9
B. 61
C. 98
D. 54
E. 64

Solution : Notice that the new cubes will be each of side 1Cm. So on any face of the old cube there will be 5x5=25 of the smaller cubes. Of these, any smaller cube on the edge of the face will have 2 faces painted (one for every face shared with the bigger cube). The number of cubes that have exacly one face painted are all except the ones on the edges. Number on the edges are 16, so 9 per face.

There are 6 faces, hence 6*9=54 smaller cubes with just one face painted.

QUESTION : Number on the edges are 16, so 9 per face.

HOW DO WE KNOW THERE ARE 16 EDGES ? AND FROM THIS HOW IS 9 CALCULATED ?

THANKS

This solution should be edited.

A cube has 12 edges, 6 faces and 8 vertices:
Attachment:

faces-edges-vertices.png [ 13.61 KiB | Viewed 65328 times ]

As for the question. Look at the image below:
Attachment:

MagicCube5x5.jpg [ 71.65 KiB | Viewed 95876 times ]
Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.

Similar questions to practice:
the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html
a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html
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a-large-cube-consists-of-125-identical-small-cubes-how-110256.html

3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html
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Re: Math : 3-D Geometries [#permalink]
Can you please explain me how i resolve this equation? I cant seem to do it right.
its from the first example:

"Solution : The volume of the liquid is constant.
Initial volume = \pi * 5^2 * 9
New volume = \pi * r^2 * 4
\pi * 5^2 * 9 = \pi * r^2 * 4
r = (5*3)/2 = 7.5"
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Re: Math : 3-D Geometries [#permalink]
Hi bogdanbb,

Your approach and solution are correct (the radius is 7.5). What part about it do you not understand?

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Re: Math : 3-D Geometries [#permalink]
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Hi bb,

None of the images are visible. Kindly check the image links. Thanks
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Re: Math : 3-D Geometries [#permalink]
wings.ap
Hi bb,

None of the images are visible. Kindly check the image links. Thanks

Thank you for reporting this. It seems the hosted images that Shrouded uploaded were deleted by the host he used.