To a first approximation, a tennis ball is a sphere. The volume of a sphere is
V = 4/3 π r3, where r is the radius of the sphere.
So measure the diameter of the tennis ball, divide by 2 to get the radius, and then apply the formula above.
You could also measure the volume of a tennis ball by measuring the volume of water that it displaces.
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They are spheres. They cannot therefore have different geometrical properties. To alter surface to volume ratios you would need to alter the shape. The study of mathematical shapes is called topology.
Knowing the diameter of the ball allows you to calculate it. Using displacement of water allows to directly calculate it. Using direct measurement eliminates the error caused by the "dimples" on the ball's surface. (The minimum legal size for a ball has a volume of about 2.482 cubic inches or 40.68 cm3.)How to computeV = 4/3 (pi) r3 (4 x 3.1416 x radius cubed)How to measureThe easiest way to check would be to put a golf ball in a beaker of water. Fill a 200 ml beaker with water, and place the ball in it. Catch the overflow in another measured beaker. Since water is almost exactly 1 ml = 1 cc, the liquid displaced by the completely submerged ball will provide a close estimate of its volume in cm3.
Volume in cubic units = pi*radius2*height
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Think of any ball you have ever held in your hand. A baseball, a softball, a tennis ball, a bowling ball - those are all spheres.