The record height of a man to date is 8 feet 11 inches {107 inches}. If all men had identical...

Question:

The record height of a man to date is 8 feet 11 inches {107 inches}. If all men had identical body types, their weights would vary directly as the cube of their heights. Assume that all men do have identical body types. If a man who is 5 feet 10 inches tall {70 inches} weighs 175 pounds, approximately how much would a man with a height of 9 feet {108 inches} weigh?

Tallest Man Ever

The Guinness world records is a book that contains the lists of the most extraordinary humans in history, which include the tallest person who ever lived. The record-holder was Robert Wadlow with a remarkable height of 8 ft and 11.1 in.

Answer and Explanation:

If the weight varies directly with the cube of height, then we have the following equation:

{eq}w=kh^3 {/eq}

where k is a constant, which represents the density of men's body. We can evaluate the value of k using the given values of height and weight.

{eq}k=\dfrac{w}{h^3}\\[0.2cm] k=\dfrac{175\,\rm lbs}{{70\,\rm in}^3}\\[0.2cm] k=\dfrac{175\,\rm lbs}{343000\,\rm in^3}\\[0.2cm] k\approx 5.1\times 10^{-4}\,\dfrac{\rm lbs}{\rm in^3}\\[0.2cm] {/eq}

Therefore, the estimated weight of a man with a height of 9 ft (108 in) would be

{eq}w=5.1\times 10^{-4}\,\dfrac{\rm lbs}{\rm in^3}(108\,\rm in)^3\\[0.2cm] \color{blue}{w\approx 642.7\,\rm lbs} {/eq}


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