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A right pyramid has a square base with area 288 square cm. Its peak is 18 cm from each of the other vertices. What is the volume of the pyramid, in cubic centimeters?

 Apr 20, 2022
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The diagonal across the base =   sqrt ( base area) * sqrt 2  =   sqrt (288) * sqrt 2 =    12 sqrt 2* sqrt 2  = 24

 

1/ 2 of  this =   12

 

18 is the slant  height

 

The true height , h  =   sqrt  [18^2  -12^2 ]   = sqrt [ 324 - 144 ]  =  sqrt 180  =  6sqrt 5

 

 

The volume is

 

base area * height /  3  = 

 

288 * 6 sqrt 5  / 3  =   

 

288 * 3sqrt 5  cm^3  ≈   1932 cm^3

 

cool cool cool

 Apr 20, 2022

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