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Hi, I've been working on a problem which I thought would be quite easy - but the answer I got was incorrect. Can someone please help me?

 

In a certain regular square pyramid, all of the edges have length 12. Find the volume of the pyramid.

 

Thank you so much!!!

 Jul 3, 2020
 #1
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the formula for the volume of a pyramid is length*width*height/3. We know the length and the width but we don't know the height. Since we know this is a regular pyramid, and we know all edges have the length of twelve, we can draw a triangle with the information we know

 height^2 + (1/2*length)^2 = k^2(where k is the length from any corner to the tip of the pyramid.) know we plug in the information we know.

height^2 + 36 = 144

height^2 =108 

height = 6 root 3.

so then we plug in those values in to the formula for a pyramid and get 12*12*6 root 3 /3

= 4*12*6root3

=48*6(sqrt108) = 1728*sqrt(3)

 Jul 3, 2020
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1)   Diagonal of a square   d = sqrt( 122 + 12) = 16.97056275            d/2 = 8.485281374

 

2)   Height of a pyramid     h = sqrt( 122 - 8.4852813742 ) = 8.485281374 (surprise)

 

3)   Volume of the pyramid     V = lwh/3 = (12*12*8.485281374) /3 = 407.293506 u3  indecision

Guest Jul 3, 2020
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Hello, Guest!

 

" height = 6 root 3 "     this is slant height

 

You need the altitude (height) of the pyramid to calculate the volume.

 

I'll use your slant height to find the height of the pyramid.

 

h = sqrt[( 6*√3)2 - 62 ] = sqrt( 108 - 36 ) = 8.485281374  smiley

Guest Jul 3, 2020
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We can use slant height this way:  V = [ 12 * 12 + (6√3) ] / √13.5 = 407.293506 u3   smiley

Guest Jul 3, 2020
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Thank you all so much!

Caffeine  Jul 5, 2020

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