What is the volume of a pyramid with slant height 25 feet and square base with edges of 14 feet?

First find the height of the pyramid.  Imagine a triangle with hypo 25 ft and base (14/2) ft.  The area of the base is 14^2 ft, or 196 ft^2.  The height of the pyramid is found using the Pythagorean Theorem:

(14/2)^2 + h^2 = 25^2, or   25^2 - 7^2 = h^2 

This, in turn, is 625-49 = 576 = h^2, so that h = +24 ft.

Therefore, the volume of this pyramid is A = (1/3)(196 ft^2)(24 ft) 
                                                                    = 1568 ft^3.

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