Calculating the Surface Area in nm^2 of a Water Solution in a 9.0 cm Petri Dish

Understanding the surface area of a solution in a Petri dish is a fundamental concept in many scientific experiments, particularly in the field of microbiology and chemistry. It is crucial for determining the amount of substance that can interact with the solution, which can significantly impact the results of an experiment. In this article, we will explore how to calculate the surface area of a water solution in a Petri dish with a diameter of 9.0 cm, expressed in nanometers squared (nm^2).

Understanding the Basics

Before we delve into the calculations, it’s important to understand some basic concepts. A Petri dish is a flat cylindrical container made of glass or clear plastic. It is commonly used in laboratories for growing cultures of microorganisms or small plants. The surface area of a Petri dish is the area of the flat circular base where the solution is placed. This is calculated using the formula for the area of a circle, which is πr^2, where r is the radius of the circle.

Converting Centimeters to Nanometers

Since the diameter of the Petri dish is given in centimeters (cm), we need to convert it to nanometers (nm) to calculate the surface area in nm^2. One centimeter is equivalent to 1 x 10^7 nanometers. Therefore, to convert the diameter from cm to nm, we multiply by 1 x 10^7.

Calculating the Surface Area

Once we have the radius in nanometers, we can calculate the surface area. The radius is half of the diameter, so we divide the diameter by 2. We then substitute the radius into the formula for the area of a circle (πr^2) to get the surface area in nm^2.

Example Calculation

Let’s calculate the surface area of a water solution in a Petri dish with a diameter of 9.0 cm. First, we convert the diameter to nanometers:

• Diameter in nm = Diameter in cm x 1 x 10^7 = 9.0 cm x 1 x 10^7 = 9.0 x 10^8 nm

Next, we calculate the radius:

• Radius = Diameter / 2 = 9.0 x 10^8 nm / 2 = 4.5 x 10^8 nm

Finally, we calculate the surface area:

• Surface area = πr^2 = π x (4.5 x 10^8 nm)^2 = 6.36 x 10^17 nm^2

So, the surface area of a water solution in a 9.0 cm Petri dish is approximately 6.36 x 10^17 nm^2.

Conclusion

Calculating the surface area of a solution in a Petri dish is a straightforward process once you understand the basic principles and conversions. This knowledge is essential for many scientific experiments and can help ensure accurate and reliable results.