# Problem: Approximate the percent increase in waist size that occurs when a 150-lb person gains 35.0 lb of fat. Assume that the volume of the person can be modeled by a cylinder that is 4.0 ft tall. The average density of a human is about 1.0 g/cm3, and the density of fat is 0.918 g/cm3.

###### FREE Expert Solution

We’re asked to determine the approximate percent increase in waist size that occurs when a 150-lb person gains 35.0 lb of fat.

We will assume that the volume of a person can be modeled by a cylinder that is 4.0 ft tall

Recall that the percent increase is given by the equation:

Since we're given the density, we can first solve for the waist size of the person to determine the percent increase by doing these steps:

Step 1. Write the equation for the volume of the person using the equation for the volume of a cylinder:

$\overline{){\mathbf{Volume}}{\mathbf{=}}{{\mathbf{\pi r}}}^{{\mathbf{2}}}{\mathbf{h}}}$

π = 3.1416 (constant)

h = height

Step 2. Determine the change in volume of the person before and after gaining fat based on the given density (of the person and fat) using the equation:

$\overline{){\mathbf{density}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}$

Step 3. Determine the % increase in waist size, by solving for the change in radius, r.

We can solve for the waist size using the equation for the circumference (assuming it is circular):

$\overline{){\mathbf{Circumference}}{\mathbf{=}}{\mathbf{2}}{\mathbf{\pi r}}}$

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###### Problem Details

Approximate the percent increase in waist size that occurs when a 150-lb person gains 35.0 lb of fat. Assume that the volume of the person can be modeled by a cylinder that is 4.0 ft tall. The average density of a human is about 1.0 g/cm3, and the density of fat is 0.918 g/cm3.