# 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:

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

r = radius

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):

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

###### 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.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Density concept. You can view video lessons to learn Density. Or if you need more Density practice, you can also practice Density practice problems.