Bacteria vary in size, but a diameter of 2.0 μm is not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size?

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Hey everyone. So today we're dealing with the rod shaped or cylinder shaped microorganism that has a unit cell length of 1.5 micrometers and a radius of 0.25 micrometers. So with this information we need to find out the volume and surface area that this microorganism takes up again. It is a rod so it is a cylinder. So let me draw a crude cylinder right here for you guys number two and bam. So it's telling us that the length is 1. μ m and that the radius point from the center to one edge of the uh faces. The top and bottom is 0.25 Microm less liberal. These are as equal to and L is equal to that. So to calculate the volume of the cylinder we'll keep it in blue for now the volume of a cylinder is calculated as pie, R squared H. So let's read that very blitz length which is also height which will serve us the same in this purpose. There's this assistance by the way. So substituting in our values because both are in micrometers, this is simply pie into 0.25 micrometers squared Into 1.5 μ Which when simplified gives a value of 0. micrometers, cute surface area is calculated slightly differently. The surface area of a cube will be two pi Rh plus two pi R squared or the latter half is the uh some of the areas of the two faces. While the first term is the sum of the rest of the cylinder. So expanding that out, we have to pie and I'll keep our variables in blue 0.25 into 1. plus two pi. And I'm leaving out the units because for the sake of simplicity in our calculations so that it looks a little more concise on writing it out here. But don't forget we're still dealing with micrometers but simplifying this, we get 2.75 micrometer squared, so the volume is 0. micro meter cubed, which eliminates answer choices A and B. And the surface area of the rod shaped microorganism is 2.75 micrometers, which means our answer is d I hope this helps. I look forward to seeing you all in the next one.

Bacteria vary in size, but a diameter of 2.0 μm is not unusual. What are the volume (in cubic centimeters) and surface area (in square millimeters) of a spherical bacterium of that size?

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Key Concepts

Volume of a Sphere

Surface Area of a Sphere

Unit Conversion