Question 1136492

A right pyramid on a base {{{4cm}}} square has a slant edge of {{{6cm}}}. Calculate the volume of the pyramid. Explain with diagram 


the half of diagonal of the base, a slant edge and height of the pyramid form right triangle where slant edge is hypotenuse, half of diagonal of the base one leg, and height of the pyramid the other leg

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first find diagonal of base:

{{{d^2 = 4^2 + 4^2}}}

 {{{d^2 = 32}}}

{{{d= sqrt(32)}}}

{{{d = 4sqrt(2)}}}


then {{{h^2=6^2 + (2sqrt(2))^2}}}

{{{h^2 = 36-8}}}

{{{h^2 = 28}}}

{{{h = sqrt(28)}}}

{{{h = 2sqrt(7)}}}


and volume is: {{{(1/3)}}}*Area of the base * Height  

Area of the base: {{{b=4cm*4cm=16cm^2}}}



{{{V= (1/3) b*h}}}

{{{V= (1/3)(16cm^2)*2sqrt(7)cm}}}

 {{{V= (32/3)sqrt(7)cm^3 }}} or approximately {{{28.22cm^3}}}