Question

What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 0.84 +_ 0.04 m?"?

Answer 1

100 * (formula with max error - formula with measured value)/ formula with measured value
multiplying by 100 in front makes it a percentage. 
In the case of r=3.86 +- 0.08 m, 
the max error is 3.86 + 0.08 = 3.94 [just add the measurement error to the measurement] 
the measured value is just 3.86 
The formula for the volume of a sphere is (4/3)*pi*r^3 where r is the radius. 
100 * (4/3 pi max error^3 - 4/3 pi measured^3) / (4/3 pi measured^3) 
100 * (4/3 pi 3.94 ^3 - 4/3 pi 3.86 ^3) / (4/3 pi 3.86 ^3) 
which reduces to 
100 * (3.94^3 - 3.86^3)/ 3.86^3 
~ 6.35%