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Spherical Percent Uncertainty and Violent Storm Question

  • #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!
 

Answers and Replies

  • #2
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4,188
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
 

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