The circumference of a scircle is measured as 56 cm with an error 0.02 cm. The percentage error in its area, is

Options

A. `1/7`
B. `1/28`
C. `1/14`
D. `1/56`

Answer

C

Explanation

Let r be the radius, C be the circumference and A be the area of the circle. Then, `C=2pirand A=pir^(2)`
`:." " DeltaC = (dC)/(dr)" " Delta r and Delta" "A=(dA)/(dr) Delta r`
` rArr" "Delta C=2pi Delta r and Delta A = 2pi r" " Delta r`
We have, `C = 56 and Delta C = 0.02`
`:. " "(DeltaC)/C=(0.02)/56=1/2800`
`rArr" "(2piDeltar)/(2pir)=1/2800rArr (Deltar)/r=1/2800`
`:." "(DeltaA)/Axx100=(2piDeltar)/(pir^(2)) xx100=2((Deltar)/r xx100)=2 xx1/28=1/14`