Chemistry: Approximate the percent increase in waist size that occurs when a 130 lb person gains 30.0 lbs of fat. assume that the volume of the person can be modeled by a cylinder that is 4.0 feet tall. the average density of a human is about 1.0 g/cm3 and the density of fat is 0.918 g/cm3

Approximate the percent increase in waist size

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2020sanchezyiczela

02.01.2022

Chemistry

11.85%

Explanation:

First of all, we need to work with the same units.

130 lb = 58967 g30.0 lb = 13607.8 g4.0 feet = 121.92 cm

The volume of a cylinder is:

a) $\textrm{V}=\pi*r^{2}*h$

And as we know, the density is the mass per unit volume.

b) $\rho = \frac{m}{V}$

With a and b we have the equation c:

c) $\rho =\frac{m}{\pi*r^{2}*h }$

$r = \sqrt{\frac{m}{\pi*\rho*h }}$

Now we can calculate the radius of the waist of the person when his weight is 130 lb.

$r =\sqrt{\frac{58967g}{3.14159* 1\frac{g}{cm^{3} }* 121.92cm} } \\\\r=12.41cm$

To calculate the radius of the fat we use the formula of the volume of a hollow cylinder because the fat wraps up our original cylinder, the formula is:

d) $\textrm{V}=\pi*(r_{2}^{2}-r_{1}^{2})*h$

with b and d we have the equation e:

e) $\rho =\frac{m}{\pi*(r_{2}^{2}-r_{1}^{2})*h }$

$r_{2}=\sqrt{\frac{m}{\pi*h*\rho} +r_{1}^{2}}$

The radius of the waist after the person gains 30.0 lbs will be:

$r_{2} = \sqrt{\frac{13607.8g}{3.14159*121.92 cm*0.918\frac{g}{cm^{3} } } +(12.41cm)^{2}}$

$r_{2}=13.88cm$

So, the percent increase in waist will be:

$\%\textrm{increase}=\frac{\textrm{increase}}{\textrm{original number}}*100\%\\\\ \%\textrm{increase} =\frac{13.88-12.41}{12.41}*100\%\\\\ \%\textrm{increase} =11.85\%$

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Approximate the percent increase in waist size that occurs when a 130 lb person gains 30.0 lbs of fat. assume that the volume of the person can be modeled by a cylinder that is 4.0 feet 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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