How Many Blades of Grass Are on a Quarter Acre of Land?

[mrserv0n]

Ok here's the question and what I have solved so far

Grass grows densely everywhere on a 1/4 acre plot of land. What is the order of magnitude of the number of blades of grass? Explain your reasoning. Note that 1 acre = 43560 ft^2.

Ok. 43560/4 to get the 1/4 acre = 10890 ft^2

Now I have no experience with order of magnitude problems yet, as I just started physics but I would guess to head in this direction.

Figure there is an estimated 1 blade of grass per cm. Convert the ft to cm and get 30.48cm in a foot so there would be 331927.20 cm in 10890 ft meaning there is 331927.20 blades of grass in the 1/4 acre if this information was accurate, so what is the +/- factor of this or the order of magnitude rather..

thanks

 

[Tide]

Your basic calculation is in error. If there are 30.48 cm in 1 foot then there are (30.48)^2 cm^2 in 1 ft^2.

 

[quicknote]

The order of magnitude of the number of blades of grass on a 1/4 acre plot of land can be estimated by breaking down the problem into smaller, more manageable parts. First, we can convert the area of 1/4 acre into square feet and then into square centimeters. This gives us a total of 10890 ft^2 or 1,010,748.64 cm^2.

Next, we can estimate the number of blades of grass per square centimeter. Since we do not have an exact number, we can make an educated guess based on our experience or research. Let's say there is 1 blade of grass per square centimeter. This means that there would be approximately 1,010,748.64 blades of grass in the 1/4 acre plot.

To determine the order of magnitude, we need to look at the number of digits in our estimate. In this case, there are 7 digits in our estimate of 1,010,748.64. Therefore, the order of magnitude would be 7. This means that the actual number of blades of grass could vary by a factor of 10^7 or 10 million.

However, it is important to note that our estimate of 1 blade of grass per square centimeter is just an assumption and may not be accurate. If we were to increase the number of blades of grass per square centimeter, the order of magnitude would also increase. For example, if we estimate 10 blades of grass per square centimeter, the order of magnitude would be 8.

In conclusion, the order of magnitude of the number of blades of grass on a 1/4 acre plot of land is approximately 7, but this can vary depending on the assumptions and accuracy of our estimates.