# Volume

The average height of a woman living in the United States is 1.622 meters (about 5 feet 3.75 inches). The average weight for a woman of this height ranges from 51.7 to 57.6 kg (about 114 to 127 lbs). To be tactful, I will use the lower bound of weight for calculation. From height and weight, body surface area can be estimated using the Du Bois formula:

$$s_{woman} = 0.007184 * (162.2\ cm)^{0.725} * (51.7\ kg)^{0.425}$$

$$= 1.54\ m^2$$

In 1966, the US Naval Medical Research Institute attempted to create a general formula for body volume using height and weight. In the process, they created a few formulas for more specific groups of people. The most relevant equation, of course, applies to women in the adolescent to adult age group. The study mentions that this formula was developed using test subjects with a weight (kg) to height (cm) ratio between .2 and .8. Luckily, the weight to height ratio of the average woman with $$\frac{51.6\ kg}{162.2\ cm} = 0.318\ \frac{kg}{cm}$$. Since the ratio is within the range, we can use the formula to approximate the volume of the average woman.

$$v_{woman} = 62.90 * (s_{woman}\ m^2) * (\frac{51.7\ kg}{162.2\ cm})^{0.578}$$

$$= 49.9\ liters$$

$$=4.99*10^{-2}\ m^3$$

Now the lunar step. The Lunar Scale Factor cubed gives the ratio of Luna’s volume to the average girl’s volume. Multiplying that by the average girl’s volume gives Luna’s volume.

$$V=\Lambda^3 * (v_{woman}\ m^3)$$

$$=1.52*10^{23}\ m^3$$

For comparison, the Earth’s volume is 1.08321*1012 km3, or 1.08321*1021 m3. By dividing, we find that Luna is $$\frac{V}{1.08321*10^{21}\ m^3}=140$$ times the size of the Earth.

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