Percent uncertainty in Volume of a beach ball?

[eddiedowen]

Homework Statement

What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r=5.60±0.05m?

Homework Equations

∏r^2

The Attempt at a Solution

 

[SteamKing]

Are you sure that pi*r^2 is the volume of a sphere?

 

[eddiedowen]

I know that pi*r^2 isn't the volume of the sphere but I couldn't remember the formula for the volume of a sphere and regardless, I'm still not sure how to find the percent uncertainty, because my physics teacher isn't very clear when explaining things and it's really difficult to get the just of what he's saying.

 

[SteamKing]

As Yogi Berra would say, you could look it up.

Obviously, you could compare the volumes of a ball where the radii are 0.05 m greater or less than a radius of 5.60 m, which is more of a beach balloon. Are you sure the radius of the ball is 5.6 m?

Or, you could take the cool approach using calculus.

 

[HallsofIvy]

Since you say "roughly", there is a rule of thumb that when quantities multiply, their percentage errors add. Since this is a volume problem, it must involve a product of three distances (and since the radius, r, is the only distance involved, radius cubed). That is, the percentage error in the volume is three times the percentage error in the radius.

 

[HallsofIvy]

Accidental double post.