the radius of a circular disk is 30 cm with a maximum error in measurment of 0.4 cm. a) use differentials to measure the maximum error in the calculated area of the disk. b) what is the estimated percentage error in measuring the calculated area of the disk? i found; 2.6667%

Expert Answers

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You need to evaluate the area of circular disk considering also the maximum error in measurment such that:

`A = pi*(r + dr)^2 = 2903.334 cm^2`

You need to expand binomial such that:

`A = pi*(r^2 + 2r*dr + (dr)^2)`

You need to open the brakets such that:

`A = pi*r^2 + 2pi*r*dr + pi*(dr)^2`

You need to estimate the maximum error in the calculated area such that:

`dA = 2pi*r*dr + pi*(dr)^2`

`dA = pi*(2*30*0.4 + (0.4)^2)`

`dA = pi*(24 + 0.16)` 

`dA ~~ 75.9 cm^2`

Hence, estimating the maximum error in the calculated area yields `dA ~~ 75.9 cm^2` .

b) You need to estimate the percentage error such that:

`(dA)/A = 75.9/2903.334 = 0.026 = 2.6%`

Hence, estimating the the percentage error in measuring the calculated area yields 2.6%.

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