Question

A designer wants to make use of a half-spherical cistern in a water system. If the cistern has a diameter of 6 feet, how many gallons of water can it hold?

Answer 1

The volume of a sphere is defined asV=4/3πr3A semi-sphere would have half the volume of a sphere with the same diameter: V=2/3πr3Also,r=D/2So, V=2/3(π)(D/2)3=2/3(π)(6ft/2)3=2/3π27ft3=56.55ft356.55ft3∗7.48051948gal1ft3=423.01galWe are only justified in keeping one significant figure, but it depends on what course this is for. If sigfigs matter: 400galIf not, this is probably sufficient:423.0gal