Question 1205296
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A right pyramid on a square base of side 4cm has a slant edge of 6cm. 
Calculate the volume of the pyramid
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<pre>
We are given that the side of the square base is 4 cm.
 
Then the diagonal of the square is {{{4*sqrt(2)}}} cm.



Draw the height (the altitude) of the pyramid from the upper vertex to the base of the pyramid.


You will get a right-angled triangle with one leg on the base as the half
of the diagonal of the square, so the length of this leg is  {{{2*sqrt(2)}}} cm long.


The hypotenuse of this right-angled triangle is 6 cm (it is the slant edge).


Hence, by Pythagoras, the altitude is  h = {{{sqrt(6^2-(2*sqrt(2))^2)}}} = {{{sqrt(36-8)}}} = {{{sqrt(28)}}}  cm.


Thus the volume of the pyramide is 

    {{{(1/3)*base_area*h}}} = {{{(1/3)*4^2*sqrt(28)}}} = {{{(16/3)*sqrt(28)}}} = = {{{(32/3)*sqrt(7)}}} = 28.221 cm^3  (approximately).    <U>ANSWER</U>
</pre>

Solved.