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# Ball Weight and Density

## How much will a ball of a given diameter in a certain material weigh?

The answer is calculated by multiplying the volume of the ball by the density of the material.

Weight = Volume * Density

#### For example, calculate the weight of a two inch diameter lead ball:

Volume = (4 * * R * R * R)/ 3, or Volume = ( 4 * Pi * Radius ^ 3 ) / 3

, Pi, a universal constant = 3.1416

4 = 12.566

R=Diameter / 2 = 2 / 2 = 1

R^3 = R * R * R = 1

12.566 x 1 = 12.566

12.566 / 3 = 4.1887 cubic inches (is the volume of a 2 inch ball)

4.1887 times the density of lead, which is 0.409 pounds per cubic inch, gives a weight of 1.713 pounds.

#### What would a three inch diameter lead ball weigh?

The radius of 1.5 inches cubed equals 3.375, times 12.566 ( 4 x ) equals 42.410, divided by three, equals 14.137 cubic inches, times 0.409 ( the density of lead ) gives 5.782 pounds.

Weight = Volume * Density

Weight = [(4 * * R * R * R)/ 3 ] * 0.409

Weight = [ ( 4 * 3.1416 * (3/2) * (3/2) * (3/2) /3 ] * 0.409

Weight = 5.782 pounds

Notice that only one inch increase in diameter caused a 4 pound increase in weight. This three inch diameter ball is more than triple the weight of the two inch diameter ball.

 Material Density ( grams / cm ^3 ) 300 Stainless Steel 8.02 Aluminum Alloy 2.73 Brass 8.47 Copper 8.91 Gray Iron 7.2 Lead 11.35 Magnesium 1.77 Monel 8.9 Steel 7.86 Titanium 4.51 Water ( liquid ) 1.00 Zinc 7.14
 Material Density ( pounds / cubic inch ) Aluminum 0.0975 Brass 0.3048 Cast Iron 0.26 Copper 0.321 Lead 0.409 Magnesium 0.0628 Steel 0.283 Titanium 0.162 Zinc 0.254

**See also: A density measurement conversion tool that is available at

http://www.easyunitconverter.com/density-unit-conversion/density-unit-converter.aspx , for density unit conversions of various materials such as brass, copper, steel, and aluminum.

http://www.convertauto.com from Lilly Hammond at NCSU.

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