Question

URGENT
the uncertanity recorded in the radius of a sphere is 1.6% .the uncertanity in the area of that sphere is?

Answer 1

The fractional uncertainty in the radius of a sphere is δrr=0.016δrr=0.016. The area of the sphere is A=4πr2A=4πr2, and its fractional uncertainty is δAAδAA, where δA=dAdrδr=8πrδrδA=dAdrδr=8πrδr. So, the fractional uncertainty in A is δAA=8πrδr4πr2=2δrr=2×0.016=0.032=δAA=8πrδr4πr2=2δrr=2×0.016=0.032=3.2%.

let me simplify the answer.

For small errors (uncertainties) you simply add 'em up.

R occurs twice in the Area formula, so 1.6+1.6 = 3.2%

It relies squares and higher powers of the errors being negligible.