The radius of a spherical ball is measured at r = 50 cm. Estimate the maximum error in the volume and surface area if r is accurate to within 0.1 cm. (Round your answers to three decimal places.)

Answer 1

0.1 cm means a 0.2% error
so, v can be off by .6% and area by 0.4%

checking for v,
4/3 π(50-0.1)^3 <= v <= 4/3 π(50+0.1)
520463.46194 <= v <= 526746.65563
v(50) = 523598.77560
so, for error e,
3135.31366 <= e <= 3147.88003
so for the relative error er
.005988 <= er <= .00601
or, 0.6%