Math CentralQuandaries & Queries


Question from sharon:

We have a cistern to hold spring water that measures 12 feet in depth by 5 feet in diameter. How much in liquid gallons will it hold?

Hi Sharon,

I remember that there are 231 cubic inches in a US gallon so I am going to change your dimensions to inches. Thus your cistern is 12 × 12 = 144 inches deep and has a radius of 5/2 × 12 = 30 inches. The volume of a right circular cylinder is

π r2 h

where r is the radius and h is the height. Thus your cistern has a volume of

π × 302 × 144 = 407,150.40 cubic inches.

Which is

407,150.40/231 = 1,762.6 US gallons.


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