A designer wants to make use of a halfspherical cistern in a

A designer wants to make use of a half-spherical cistern in a water system. If the cistern has a diameter of 7.5 feet, how many gallons of water can it hold? Note: Use US gallons.

Solution

volume of half sphere =(2/3)r³, where r is radius

given cistern has a diameter of 8 feet=> radius =7.5/2 =3.75 feet

volume of half-spherical cistern =(2/3)3.75³

volume of half-spherical cistern =(128/3)

volume of half-spherical cistern =110.4466 ft³

1ft³=7.48052 gallons

number of gallons of water it can hold =110.4466*7.48=826.14 gallons