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.

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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:


%Increase=increase in waist sizeoriginal waist size


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:


Volume=πr2h


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: 


density=massvolume


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):

 

Circumference=2πr


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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.

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