Chapter 1.3, Problem 1.4AFP

Interpretation Introduction

Interpretation:

The volume of a ribosome particle whose diameter is $21.4\text{ nm}$ in ${\text{dm}}^{\text{3}}$ and $\text{μL}$ is to be calculated. Also, a road map for the solution is to be drawn.

Concept introduction:

Volume is a physical quantity and its SI unit is cubic meter $\left({\text{m}}^{\text{3}}\right)$. The volume of an object is equal to the product of the height, length, and breadth of the object. Length, breadth, and height of an object is measured in the units of length. Therefore, volume has the unit of length to the cubic power. The other unit of volume are liter, milliter, cubic decimeter, microliter.

The conversion of one unit into another can be done using a proper conversion factor. Conversion factors are the ratios that relates the two different units of a quantity. It is also known as dimensional analysis or factor label method.

In the unit conversion problems, the given information is multiplied by the conversion factors to obtain the desired information. The unit conversion can be done as follows:

$\left(\cancel{\text{beginning unit}}\right)\left(\frac{\text{Final unit}}{\cancel{\text{beginning unit}}}\right)=\text{Final unit}$

The relation between diameter and radius is,

$\text{radius}\left(r\right)=\frac{\text{diameter}\left(d\right)}{2}$

The formula to calculate the volume is,

$\text{Volume}=\frac{4}{3}\pi r^3$