`S=4pir^2` If the `C=82cm, C=2pir` , So `r = 82/(2pi) = 41/pi`
`S = 4pi(41/pi)^2 = 4pi*41^2/pi^2 = 4*1681/pi = 6724/pi`
` S=4pi(C/(2pi))^2=4piC^2/(4pi^2)=C^2/pi`
` DeltaS=(2C)/pi DeltaC`
is a linear approximation for the error in S
`DeltaS = (2(82))/pi (0.5) = 82/pi` cm this an estimate of the...
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`S=4pir^2` If the `C=82cm, C=2pir` , So `r = 82/(2pi) = 41/pi`
`S = 4pi(41/pi)^2 = 4pi*41^2/pi^2 = 4*1681/pi = 6724/pi`
` S=4pi(C/(2pi))^2=4piC^2/(4pi^2)=C^2/pi`
` DeltaS=(2C)/pi DeltaC`
is a linear approximation for the error in S
`DeltaS = (2(82))/pi (0.5) = 82/pi` cm this an estimate of the maximum error in S
The relative error is `(82/pi)/(82^2/pi)^2 = pi/82`