Percent uncertainty in the volume of a spherical beach ball

[Anamoly]

Question is : What is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 3.86 ± 0.08 m ?

The answer is 6 % , but I am not getting that, I am pretty sure I am on the right path, I found the volume of the ball using V = (4 x 3.14 x r^3) / 3

Btw, I am pretty sure you need to take into account the ± .08m for 3.86 when you find radius. I got 3.94 and 3.78 Radius's. But I still don't see how I can get 6 %. Heres the percent uncertainty formula. (uncertainty)/(value) x 100

Maybe I am on the wrong track, please help me through this problem, I am new to Physics and a little rusty on my math, so any pointers are greatly appreciated.

Thanks
-Anamoly

 

[jcsd]

If you get in trouble with these questions, one idiot p-proof method is to work out the volume: with a) the measured value, b) the maximum value, c) the minimum value, then by comapring the volumes the uncertainty is obvious.

 

[Anamoly]

a) V=240
b) V=256
c) V=226

Please point out the obvious.

(I know the answer, I just want some help how to find it.)

 

[jcsd]

(max. - min.)/2 then just divide and mutiply by 100 to get the answer in percent.

 

[Nenad]

?
Here is how you do it:

$$uncertainty = \frac{V_{u}- V_{e}}{V_{e}} * 100$$

$$uncertainty = \frac{256 - 240}{240} * 100$$

$$uncertainty = 6.66$$

Does that answer your question.

 

[Nenad]

there we go, sorry for all of the posts, I had a big error, the answer is 3 posts up.

 

[Raza]

$$V=\frac{4}{3} \pi r^3$$

$$dV=\frac{4}{3}(3r^2) \pi$$

$$dV=\frac{4}{3}(44.6988) \pi \times (0.08)=14.97971165$$

$$\frac{14.97971165}{256} \times 100 = 5.8$$

 

[russ_watters]

Do you realize this thread is more than 4 years old...?

 

[gmax137]

Do you realize this thread is more than 4 years old...?

Russ - "what happens online, STAYS online..." apparently forever. That's the beauty & the curse of the medium.

 

[Raza]

Do you realize this thread is more than 4 years old...?

woah, I am completely sorry.
I was just searching in Google and found this. I didn't realize that it would be that old.
BTW, people who were searching like me now know the answer.

 

[whulj2006]

$$V=\frac{4}{3} \pi r^3$$

$$dV=\frac{4}{3}(3r^2) \pi$$

$$dV=\frac{4}{3}(44.6988) \pi \times (0.08)=14.97971165$$

$$\frac{14.97971165}{256} \times 100 = 5.8$$

I agree with that!

 

[BeerGUT]

6 years later and still useful.

 

[kLPantera]

Almost 7 years later and we just did this problem in class! Still useful.