Question

A square pyramid resting on its base is filled to half it's height with 320cubic cm of water. How much water is needed to finish filling the pyramid?

Answer 1

The formula for solving volume of a square pyramid is:
Volume = 1/3*h*b²

Solving for the remaining space to be filled up:
320 = 1/3*h*b² - 1/3*(h/2)(b/2)²
320=1/3hb² - 1/3h/2b²/4
320= 1/3 (7/8hb²)
Divide both sides by 7/8:
320(8/7)=1/3hb²
Volume = 45.714 cm³