Q13E - University Physics with Modern Physics

Question

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.)

Step-by-Step Solution

Answer

Given

Bacteria Diameter =$2.0\mu m$

Radius $r= 1\mu m$

Step1(Calculation of Volume in cubic centimeters)

As we know that 

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

=$\frac{4}{3}\left(3.14\right){\left(1\right)}^3$

Volume of bacteria= $4.19\times {10}^{-12}c{m}^3$

Step 2(Calculation of surface area of bacteria in millimeter square)

Surface area=  $4{\mathrm{\pi r}}^2$

$=4\times 3.14{\left(1\right)}^2$

Surface area $=1.26\times {10}^{-5}m{m}^2$

Step3(Conclusion)

Volume of bacteria $=4.19\times {10}^{-12}c{m}^3$ and Surface area $=1.26\times {10}^{-5}m{m}^2$.