Question

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.

Answer 1

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.