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

 Sep 11, 2020
 #1
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The volume works out to 144*sqrt(5).

 Sep 11, 2020
 #2
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Lets use (a^2)*(h/3).

h is calculated by finding the square’s diagonal (√(12^2 + 12^2) which comes to √288 or 12√2. 

So, from the corner to the centre of the square is 6√2. This gives a right triangle with hypotenuse of 12 and base of 6√2.
12^2 - (6√2)^2 = 144 - 72. Therefore, the perpendicular height is √72 which is 6√2.

Plug that into the formula and get 144*((6√2)/3) which gives 144*(2√2) or 288√2.

A close decimal equivalent is 407.3 units^3

 

Hope that helps!!

 Sep 11, 2020
 #3
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that didn't work

qwertyzz  Sep 13, 2020
 #4
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Then your question is not correct!!!

 

edge * edge * height / 3 = volume

 

1st answer is not correct but the 2nd is.

Guest Sep 13, 2020

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