Spherical Percent Uncertainty and Violent Storm Question

In summary: 8 km x 10 km x 1.1 cm x 1 m/100 cm x 1 m/100 cm x 1 m/100 cm x 1000 kg/m^3 x 10^6 cc/m^3 x 1 metric ton/1000 kg = 8.8e8 metric tons.
  • #1
Q1: What is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 3.85 plus or minus 0.06 m?

I found the volume of the original sphere, as well as one with a radius of 3.91. I then subtracted the volumes to find the difference between the two, divided that by the volume of the original sphere, then multiplied that by 100 to get 4.7%, but it was wrong.

Q2: A violent rainstorm dumps 1.1 cm of rain on a city 8 km wide and 10 km long in a 2 h period. How many metric tons (1 ton = 103 kg) of water fell on the city? (1 cm3 of water has a mass of 1 gram = 10-3 kg.)

I found the answer to be 8.8e8 tons, which turned out to be wrong. I worked out another problem like this on my homework, but I don't know whether the answer is right or wrong yet, but I'm having trouble with these, and help would be greatly appreciated. Thanks!
 
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  • #2
berenmacbowma said:
Q1: What is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 3.85 plus or minus 0.06 m?

I found the volume of the original sphere, as well as one with a radius of 3.91. I then subtracted the volumes to find the difference between the two, divided that by the volume of the original sphere, then multiplied that by 100 to get 4.7%, but it was wrong.

Q2: A violent rainstorm dumps 1.1 cm of rain on a city 8 km wide and 10 km long in a 2 h period. How many metric tons (1 ton = 103 kg) of water fell on the city? (1 cm3 of water has a mass of 1 gram = 10-3 kg.)

I found the answer to be 8.8e8 tons, which turned out to be wrong. I worked out another problem like this on my homework, but I don't know whether the answer is right or wrong yet, but I'm having trouble with these, and help would be greatly appreciated. Thanks!

The 4.7% is correct. You can get this result the way you did, or by getting the linear uncertainty, and multiplying by 3.

In the second question, it looks like you made a made a mistake on units (factors of 10).
10^6 cc = 1 m^3
1000 kg = 1 metric ton
 

1. What is spherical percent uncertainty?

Spherical percent uncertainty is a measure of the uncertainty or error associated with a measurement in three-dimensional space. It takes into account the uncertainty in all three dimensions, rather than just one or two.

2. How is spherical percent uncertainty calculated?

Spherical percent uncertainty is calculated by dividing the uncertainty in the measurement by the actual value, and then multiplying by 100 to express it as a percentage. This is typically done for all three dimensions and then added together to get the total spherical percent uncertainty.

3. Why is spherical percent uncertainty important?

Spherical percent uncertainty is important because it allows us to understand the accuracy of our measurements in three-dimensional space. It helps us to determine the reliability of our data and make informed decisions based on the uncertainty associated with it.

4. How does spherical percent uncertainty relate to violent storms?

In the context of violent storms, spherical percent uncertainty can be used to measure the accuracy of forecasting models. By understanding the uncertainty associated with various data points, scientists can make more accurate predictions about the path and intensity of a storm.

5. Can spherical percent uncertainty be reduced?

Spherical percent uncertainty cannot be completely eliminated, but it can be reduced by improving the precision of measurements and reducing sources of error. This can be achieved through better equipment, techniques, and data analysis methods.

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