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The question is what is the volume of a square pyramid with base edges of 40 cm and a slant height of 25 cm.


The Volume, V,  of a pyramid is V = [1/3] * area of the base * height


The base of this pyramid is a square of side 40 cm, then its area is (40cm)^2 = 1600 cm^2

The height of the pyramid is calculated using Pytagora's theorem:

(half side of the base)^2  + (height of the pyramid)^2 = (slant height)^2

=> (height of the pyramid)^2 = (slant height)^2 - (half side of the base)^2


(height of the pyramid)^2 = (25cm)^2 - (20cm)^2 = 225 cm^2


=> height of the pyramid = 15 cm


Now you can calcualte the volume of the pyramid with the formula V = [1/3](area of the base)(height)


V = [1/3](1600 cm^2)(15 cm) =   8000 cm^3


Answer: 8000 cm^3
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