Bacteria vary in size, but a diameter of 2.0 is not unusual. What are the volume (in cubic centi

step 1 In this problem, we want to solve for the volume and surface area of a spherical bacteria. So we

Bacteria vary in size, but a diameter of 2.0 is not unusual....

Bacteria vary in size, but a diameter of 2.0 $\mu$m is not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size? (Consult Appendix B for relevant formulas.)

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Key Concepts

Sphere Geometry

This concept involves understanding the mathematical properties of a sphere, including its symmetry and the geometric definitions that allow the calculation of its volume and surface area. Knowing the shape’s geometry is essential for applying the appropriate formulas accurately.

Volume Formula

The volume of a sphere is calculated using the formula V = (4/3)?r³, where r is the radius. This formula is central to determining how much three-dimensional space the sphere occupies.

Surface Area Formula

The surface area of a sphere is determined by the formula A = 4?r². This formula provides the measure of the total area covering the outer surface of the sphere, which is important in understanding the extent of contact with the environment.

Unit Conversion

Unit conversion is critical when measurements are provided in one system (such as micrometers) and need to be converted to other systems like cubic centimeters or square millimeters. Consistent units are necessary to ensure accurate calculations and comparisons across different scales.

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