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=Radius

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.

**Common Ball Material Density ( Metric Units )**
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

**Common Ball Metal Density ( English Units )**
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, Sphere Mathematics

**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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