volume

 

Find the volume of the square pyramid, given its slant height​     

 

The volume of a square pyramid is found using the formula: V = (1/3) * base area * height, or V = (1/3) * s² * h, where 's' is the side length of the square base and 'h' is the height of the pyramid.     

 

Not too hard, all we need is the height.  Drop a perpendicular from the apex to the center of the base.  That's the height.  From that center point, draw a line across the square base over to the bottom of the slant height.  That's one leg of a right triangle and the slant height is its hypotenuse.  From those two sides, we can find the third side which is the height.  Thank you, Pythagoras.     

 

Remember that in a right triangle c² = a² + b² which means that b² = c² – a²     

 

(height)²  =  30² – 16²  =  900 – 256  =  644   

height  =  sqrt(644)  =  25.377     

 

V  = (¹/₃) • (32)² • 25.377  =  8662.02 cm³     

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