# How do you approximate the percent increase in waist size that occurs when a 155 lb person gains 38 lb of fat?

##### 1 Answer
Jun 16, 2018

I got between 11% and 12%

#### Explanation:

Using a bunch of ridiculous assumptions:
[1] Volume of body is proportional to average cross-section area (the height doesn't change and the weight gain is distributed equally over the entire body).
[2] Weight is proportional to volume of body.
[3] Waist is approximately a circle.

The circumference of a circle (the waist size) is proportional to the square root of the cross sectional area.

The ratio of the cross sectional area after weight gain to the cross sectional area before weight gain is $\left(155 + 38\right) : \left(155\right)$ or $\frac{193}{155}$

So the waist size (diameter) after the weight gainshould be (approximately) $\sqrt{\frac{193}{155}}$ times what it was before the weight gain.

Using a calculator, we can find that $\sqrt{\frac{193}{15}} \approx 1.115867954$

for an increase of 0.115867954~~11.6%