Math CentralQuandaries & Queries


Question from Candonn:

I have a cement silo that is 30 ft. high and has a diameter of 12 ft. I was wondering what the capacity of the silo is in tons of dry material. The silo is flat on the bottom also.

Thank You.


The volume of a cylinder is π r2 h where r is the radius, h is the height and π is approximately 3.1416. Your cylindrical silo then has volume

π (12/2)2 × 30 = 3,393 cubic feet.

The capacity in tons of dry material depends on the density of the material, the number of pounds per cubic foot. For example I went to the SIMetric site in the UK and found the density of wheat to be 769 kilograms per cubic meter. I then used Google and typed 769 kilograms per cubic meter to pounds per cubic foot into Google's search window and got the reply (769 kilograms) per (cubic meter) = 48.0071017 pounds per (cubic foot). Thus your silo would hold 3,393 × 48 = 162,860 pounds of wheat which is 162,860/2,000 = 81.4 tons.


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