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?

The volume of a sphere is defined as V = 4/3 π r3 A semi-sphere would have half the volume of a sphere with the same diameter: V = 2/3 π r3 Also, r=D/2 So, V = 2/3 (π) (D/2) 3 = 2/3 (π) (6ft/2) 3 = 2/3 π27f t3 = 56.55f t3 56.55f t3 ∗ 7.48051948gal 1f t3 = 423.01gal We are only justified in keeping one significant figure, but it depends on what course this is for. If sigfigs matter: 400gal If not, this is probably sufficient: 423.0gal