Question

What, roughly, is the percent uncertainty in the volume of a spherical beach ball whose radius is r = 2.86 plus or minus .09 m?

Answer 1

The volume of a sphere is calculated through the equation,
  
       V = 4πr³ /3
where r is the radius of the given. 

If the radius is 2.86, we can substitute the value to the equation above such that,
         V = 4π(2.86)³ / 3 = 97.99π m³

When the radius is 0.09 m plus the given radius then,
       V = 4π(2.86 - 0.09)³ / 3 = 89.03π m³

The difference between the volumes is equal to,
       difference = 97.99π - 89.03π m³ = 8.96π m³

Dividing this to the original volume and multiplying by 100%,
    percentage = (8.96π/97.99π) x 100% 
    percentage = 9.14%.

Hence, the expected percent uncertainty is equal to 9.14%.