Question 1193447
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Find the volume of a square pyramid if each base edge and each lateral edge equals 36 cm.
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            The solution by  @MathLover1 is  INCORRECT.


            I came to bring a correct solution.



<pre>
The volime of the pyramid is  one third the product of the base area by the height

    V = {{{(1/3)*36^2*h}}}.


To find the height, draw the altitude of the pyramide from its peak vertex to the center of the base square.


You have right-angled triangle, formed by the altitude, the edge of the pyramid and half of the diagonal.


From Pythagoras, the height of the pyramid is  {{{sqrt(36^2 - (36/sqrt(2))^2)}}} = {{{36/sqrt(2)}}}.


Therefore, the volume of the pyramid is

    V = {{{(1/3)*(36^3/sqrt(2))}}} = {{{36^3/(3*sqrt(2))}}} = 10996.92 cm^3  (rounded).    <U>ANSWER</U>
</pre>

Solved.



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She edited her post after seeing my solution.