Math CentralQuandaries & Queries


Question from Jared:

What is the formula for the weight of a cylinder (not hollow) made of cast iron if it has a height of 5.25 inches and a diameter of 1.75 inches?

Hi Jared,

The volume of a cylinder is the area of the base times the height. The base of your cylinder is a circle with radius $\large \frac{1.75}{2} \normalsize = 0.875$ inches and height 5.25 inches so its volume is

\[\pi\; \times 0.875^2 \times 5.25 \mbox{ cubic inches.}\]

There are 12 inches in a foot and hence $12^3$ cubic inches in a cubic foot and hence divide the volume in cubic inches by $12^3$ to calculate the volume in cubic feet.

According to the Engineering Toolbox the density of cast iron is between 425 and 487 pounds per cubic foot. Multiply the volume in cubic feet by the density to obtain the weight in pounds.


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