Question

the measured radius of a ball is 50mm with possible ±0.1 mm error. if this radius is used to calculate the volume and surface area of the ball , what are the propagated errors?

Answer 1

Find the surface area of the ball by using the formula:

S = 4 πr²

  =4 π(50)²

 =31428.57 mm²

Find the volume of the ball by using the formula:

V = (4/3) πr³

  =(4/3)  π(50)³

 =523809.524 mm³

Find the propagated errors.

dS/dt = d/dt (4 πr²) = 8πr (dr/dt)

   dS  = 8πr (dr)

          = 8π(50) (±0.1)

         =± 125.7143 mm²

dV/dt = d/dt ((4/3) πr³) = 4πr²(dr/dt)

   dV  = 4πr² (dr)

          = 4π(50)² (±0.1)

         =± 3142.86 mm²