# Converting Units: Apple and Cranberry Barrels, Cloud Water Volume and Mass

• lozek
In summary, the conversation discusses two types of "barrel" units used in the 1920s in the United States and the discrepancy in shipment volume when a customer receives cranberry barrels instead of apple barrels. It also talks about the number of water droplets and their volume in a cumulus cloud and the mass of water in the cloud. The conversation provides guidance on how to solve the problems and discusses conversions between different units.
lozek
I realize these may be easy to some of you, but I'm have a few issues. For the first one:

Two type of "barrel" units were in use in the 1920s in the United States. The apple barrel had a legally set volume of 7056 cubic inches. The cranberry barrel, 5826 inches. If a merchant sells 50 cranberry barrels of goods to a customer who thinks he is receiving apple barrels, what is the discrepancy in the shipment volume in liters?

The first disrepancy(in cubic inches) I get 61500. I multiplied both volumes by 50 and took the difference, was this the right approach? I then converted this number 61500 to L and got 1.007L which is not correct. hmm

2. A cubic centimeter in a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of 10 µm. For that range, give the lower value and the higher value, respectively, for the following.

(a) How many cubic meters of water are in a cylindrical cumulus cloud of height 2.5 km and radius 1.5 km?
to m3
(b) How many 1 liter pop bottles would that water fill?
to bottles
(c) Water has a mass per unit volume (or density) of 1000 kg/m3. How much mass does the water in the cloud have?

Do I use the v=PIxr^2xh formula to compute the volume asked for in part A? I have a feeling I'll be plugging in 50 and 500 for max and min values somewhere bu thonestly I don't even know where to start in this problem. Any help would be hihgly appreciated!

Hello Lozek. For the first one, I would just calculate the difference in cubic inches per barrel and then just multiply by 50. But we get the same thing: 61500 cubic inches. Now, there are 61.024 cubic inches in a liter. Just looking at the two numbers, can you see that 61500 cubic inches is about 1000 liters? You know, I got about "61" thousand and each liter has about 61 cubic inches. Can you figure out how much exactly?

For the second one, we worked a similar one but didn't go down to bottles although I did want to figure bucket fulls but I digress. Click this link:

The first disrepancy(in cubic inches) I get 61500. I multiplied both volumes by 50 and took the difference, was this the right approach? I then converted this number 61500 to L and got 1.007L which is not correct. hmm
61500 cu in is what I get. Show your work for the conversion so we can find where you went wrong.

Do I use the v=PIxr^2xh formula to compute the volume asked for in part A? I have a feeling I'll be plugging in 50 and 500 for max and min values somewhere bu thonestly I don't even know where to start in this problem. Any help would be hihgly appreciated!

$v = \pi r^2h$ is the volume of a cylinder with radius r and height h. You know one droplet of water has a radius of 10 micrometers, its asking you how many water droplets fit in a 2.5km x 1.5km cloud. Alot of conversions in this one.

## What is the purpose of "changing units" in scientific calculations?

The purpose of changing units in scientific calculations is to convert measurements from one unit to another in order to make comparisons, perform calculations, and communicate data more easily.

## How do you convert between units in scientific calculations?

To convert between units, you must use conversion factors and multiply or divide the original value by the appropriate conversion factor. You can also use unit conversion tables or online unit converters for quick and accurate conversions.

## Why is it important to use standard units in scientific calculations?

Using standard units in scientific calculations ensures consistency and accuracy in data analysis and communication. It also allows for easier comparison and replication of results between different experiments and researchers.

## What is the difference between metric and imperial units?

Metric units are based on the International System of Units (SI) and are used globally in scientific and technical fields. Imperial units are based on historical measurements and are primarily used in the United States and a few other countries. Metric units are more precise and easier to convert between, while imperial units are often more familiar to non-scientists.

## Can you convert between different types of units, such as length and volume?

No, you cannot convert directly between different types of units. For example, you cannot convert between meters (length) and liters (volume) without knowing the density of the substance. However, you can use conversion factors to convert between related units, such as meters and centimeters, or liters and milliliters.

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