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:
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:
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):
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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