The circumference of a sphere was measured to be 88000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.
Estimate the relative error in the calculated surface area.
2 answers
Oops the 88000 is supposed to be 88 cm and 0.5 cm
Circumference, C=88 cm
C = 2πr
Area, A=πr²
Differentiating:
dA/dr = 2πr
Using linear approximation:
δA = 2πr δr
=2πr δr
=C δr
=88 cm * 0.5 cm
=44 cm²
C = 2πr
Area, A=πr²
Differentiating:
dA/dr = 2πr
Using linear approximation:
δA = 2πr δr
=2πr δr
=C δr
=88 cm * 0.5 cm
=44 cm²
1 answer