Question

Within a cell, proteins are synthesized on particles called ribosomes.Assuming ribosomes are generally spherical, what is the volume (in dm' and μL) of a ribosome whose average diameter is 21.4 nm (V of a sphere=4/3 πr³)?

Answer 1

$V = \frac{4}{3} \pi r^3 \\ r = \frac{d}{2} = \frac{21.4 \;nm}{2} = 10.7 \;nm \\ V = \frac{4}{3} \times 3.14 \times (10.7)^3 \\ = \frac{4}{3} \times 3.14 \times 1225.043 \;nm^3 \\ = 5128.846 \;nm^3$

Convert nm³ to dm³ (L):

$5128.846 \;nm^3 \times (\frac{1 \;m}{10^9 \;nm})^3 \times (\frac{10^2 \;cm}{1 \;m})^3 \times (\frac{1 \;L}{10^3 \;cm^3}) = 5.128 \times 10^{-21} dm^3 \; or \;L$

Convert to $\mu L$ :

$5.128 \times 10^{-21} \;L \times \frac{10^6 \; \mu L}{1 \;L} = 5.128 \times 10^{-15} \; \mu L$