Answer:
11.85%
Explanation:
First of all, we need to work with the same units.
The volume of a cylinder is:
a) [tex]\textrm{V}=\pi*r^{2}*h[/tex]
And as we know, the density is the mass per unit volume.
b) [tex]\rho = \frac{m}{V}[/tex]
With a and b we have the equation c:
c) [tex]\rho =\frac{m}{\pi*r^{2}*h }[/tex]
[tex] r = \sqrt{\frac{m}{\pi*\rho*h }}[/tex]
Now we can calculate the radius of the waist of the person when his weight is 130 lb.
[tex]r =\sqrt{\frac{58967g}{3.14159* 1\frac{g}{cm^{3} }* 121.92cm} } \\\\r=12.41cm[/tex]
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) [tex]\textrm{V}=\pi*(r_{2}^{2}-r_{1}^{2})*h[/tex]
with b and d we have the equation e:
e) [tex]\rho =\frac{m}{\pi*(r_{2}^{2}-r_{1}^{2})*h }[/tex]
[tex]r_{2}=\sqrt{\frac{m}{\pi*h*\rho} +r_{1}^{2}}[/tex]
The radius of the waist after the person gains 30.0 lbs will be:
[tex]r_{2} = \sqrt{\frac{13607.8g}{3.14159*121.92 cm*0.918\frac{g}{cm^{3} } } +(12.41cm)^{2}}[/tex]
[tex]r_{2}=13.88cm[/tex]
So, the percent increase in waist will be:
[tex]\%\textrm{increase}=\frac{\textrm{increase}}{\textrm{original number}}*100\%\\\\ \%\textrm{increase} =\frac{13.88-12.41}{12.41}*100\%\\\\ \%\textrm{increase} =11.85\%[/tex]
