Find the slant height of a pyramid with a volume of 432 ft^3 if the base is a square with a side length of 12 ft.

The formula of the volume of a square pyramid is:

Volume = a^2 (h/3)

432 = 12^2 (h/3)

432 = 48h

h = 9 ft.

But we need to find the slant height.

The slant height forms the hypotenuse of the vertical height and half the base.

slant height = square root (height^2 + base^2)

sh = square root (9^2 + 6^2)

sh = square root (117)

sh = 10.82 ft

So the slant height is equal to 10.82 feet.