Volume and surface area of a football?

Answer 1

Answer assuming that by 'football' you meant one used for soccer:

Volume of a sphere (the football) = 4/3*pi*radius3

Surface area of a sphere = 4*pi*radius2

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Answer assuming that by 'football' you meant one used for American football:

Using the dimensions given on Wikipedia for a standard American football (length of ~11 inches and a central circumference of ~22 inches), one can see that the central radius is approximately 3.5 inches.

Further assuming that the shape of an American football in long cross-section is roughly that of a Vesica Piscis, one can integrate using the curve produced to yield either surface area or volume contained. Such integrations are particularly easy and straight forward to perform using a numerical approach such as by using a spreadsheet application, like Microsoft Excel.

The approximate volume and surface area of a standard football are 232 cubic inches and 189 square inches, respectively.

If one wanted to make a rough empirical check of this volume calculation, a properly inflated standard football could be immersed in water and the the displacement carefully measured. Checking the surface area would involve a bit more work but could be accomplished, again roughly, by deflating the ball and cutting it into triangular pieces that individually lie flat; which could then be measured and their collective surface areas summed up.