Bacterial volume. A bacteria is like a cylinder with length \(4 \mu \mathrm{m}\), and radius \(1 \mu \mathrm{m}\). (a) Find its volume in \(\mu \mathrm{m}^{3}\). (b) Find its volume in \(m^{3}\). (c) Find its volume in liters.

To calculate the volume of a bacterial cell shaped like a cylinder, we use the cylinder volume formula. This formula is given by: \( V = \text{π}r^2h \) where \(V \) is the volume, \(r \) is the radius, and \(h \) is the height (or length) of the cylinder.
\(\text{π} \), or pi, is approximately 3.14159.

The radius (r) is the distance from the center of the base to the edge, and the height (h) is the length of the cylinder.
Using this formula helps us find the volume in a given unit, such as cubic micrometers (\(\text{\textmu m}^3\)).
It's important to keep the units consistent while performing these calculations. Be sure to substitute the correct values of \(r \) and \(h \) into the formula.

Unit conversion is the process of changing a quantity expressed in one set of units to another.

In this exercise, we start with the volume in cubic micrometers (\(\text{\textmu m}^3\)) and convert it to cubic meters (\(m^3\)).
Afterward, we convert cubic meters (\(m^3\)) to liters (L).

When converting from one unit of volume to another, remember:

• 1 cubic micrometer (\(1 \text{\textmu m}^3\)) = \(1 \times 10^{-18} m^3\) since \(1 \text{\textmu m} = 1 \times 10^{-6} m\).
• 1 cubic meter (\(1 m^3\)) = 1000 liters (L).

Understanding these conversions is key when moving from a microscopic scale (micrometers) to a macroscopic scale (liters).

Bacterial dimensions are often given in micrometers (\(\text{\textmu m}\)).

To convert these measurements to meters (m), use the factor: \(\text{1 micrometer (\text{\textmu m}) = 1 \times 10^{-6} meters (m)}\).

For example, if a bacterium is 4 micrometers in length, that would be:
\( 4 \times 10^{-6} \text{ meters (m)}\)
Converting micrometers to meters is essential for calculations that require standard unit usage such as in cubic meters (\(m^3\)).

This step simplifies understanding and comparing with larger volumes. Always remember to convert each measurement individually and ensure your units are squared (for areas) or cubed (for volumes) as needed.

To express the volume in liters, it's important to know that one cubic meter is equivalent to 1000 liters.

The conversion formula is:
\(\text{Volume in liters} = \text{Volume in cubic meters (m}^3\text{)} \times 1000\)

For instance, after converting the obtained volume of \(12.56636 \times 10^{-18} m^3\)
to liters, the result will be: \(12.56636 \times 10^{-18} m^3 \times 1000 = 12.56636 \times 10^{-15} L\).

This step helps to translate small volumes into more familiar and manageable units like liters, making it easier to comprehend even very tiny bacterial volumes.