question: square pyramid vertical height
pyramid with square base: The side of a square base is 42 inches, the slant height is 32 inches.
Find the vertical height and the volume!
answer: square pyramid vertical height
1. step: given/wanted
side a = 42 inches
slant height (hs) = 32 inches
wanted: vertical height (hv) and volume!
2. step: calculate
vertical height = √hs² – (a/2)²
vertical height = √(32² – 21²)
vertical height = 24,15 inches
volume = a² * hv : 3
volume = 42² * 124,15 : 3
volume = 73 000,2 in3