Question

Assuming Biological substances are 90 percent water and the density of water is 1.0 x 10^3 kg/m^3, estimate teh masses (density multiplied by volume) of the following.
a. a spherical cell with a diameter of 1.0 um (volume = 4/3 pi(r^3)
b. a fly, which can be approximated by a cylinder 4.0 mm long and 2.0 mm in diameter (volume = 1pi(r^2)

Answer 1

a)\[V=\frac{ 4 }{ 3 }\pi r^3=\frac{ 4 }{ 3 }\pi \left( \frac{ d }{ 2 } \right)^3=\frac{ \pi }{ 6 }d^3\]\[d=1 \mu m=10^{-6}m\]\[V=\frac{ \pi }{ 6 }(10^{-6})^3=\frac{ \pi }{6 }*10^{-18} m^3\]
\[m=\rho V=10^3*10^{-18}*\frac{ \pi }{ 6 }=\frac{ \pi }{ 6 }*10^{-15} kg\]

Answer 2

b)
\[V=h \pi r^2=4*10^{-3}*\pi*(2*10^{-3})^2/4=4 \pi*10^{-9}\]\[m=\rho*V=4 \pi *10^{-6} kg\]

Answer 3

Do you agree with that? You can also convert it to the grams ar different fractions of kg

Answer 4

I am confused for b?

Answer 5

isn't the radius 1 since diameter is 2 so wouldn't you square that?

Answer 6

\[r^2=\left( \frac{ d }{ 2 } \right)^2=\frac{ d^2 }{ 4 }\]