Answer
$$13 \%$$
Work Step by Step
1. Convert the units to g and cm:
$$155 \space lb \times \frac{1000 \space g}{2.20 \space lb} = 70500 \space g$$ $$40.0 \space lb \times \frac{1000 \space g}{2.20 \space lb} = 18200 \space g$$ $$4.0 \space ft \times \frac{30.48 \space cm}{1 \space ft} =
120 \space cm$$
2. Calculate the volume of the person and the fat:
$$70500 \space g \times \frac{1 \space cm^3}{1.0 \space g} = 70500 \space cm^3$$ $$18200 \space g \times \frac{1 \space cm^3}{0.918 \space g} = 19800 \space cm^3$$
$$V_{person} = 70500 \space cm^3$$ $$V_{person} + V_{fat} = 70500 \space cm^3 + 19800 \space cm^3 = 90300 \space cm^3$$
3. The volume of a cylinder is calculated by the formula: $$V = \pi r^2 h$$
Solving for $r$: $$r = \sqrt {\frac V {\pi h}}$$
- Find the radius of the person without the fat:
$$r = \sqrt {\frac {(70500 \space cm^3)} {\pi (120 \space cm)}} = 13.675 \space cm$$
- Find the radius of the person with the fat:
$$r = \sqrt {\frac {(90300 \space cm^3)} {\pi (120 \space cm)}} = 15.477 \space cm$$
4. The waist size is determined by $2\pi r$. Since $2\pi$ is constant, the percent increase in waist size is equal to the same of the radius.
$$Percent \space increase = \frac{(15.477 \space cm - 13.675 \space cm)}{13.675 \space cm} \times 100\%= 13\%$$
