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Question
The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:
Relative error
Solution
We know that Area of the circular plate A(r) = πr2, A'(r) = 2πr
Change in Area = A’(12.5)(0.15) = 3.75π cm2
Exact calculation of the change in Area = A(12.65) – A(12.5)
= 160.0225π – 156.25π
= 3.7725π cm2
Relative error = `("Actual value" - "Approximate value")/"Actual value"`
= `(3.7725pi - 3.75pi)/(3.7725pi)`
= `(0.0225pi)/(3.7725pi)`
= 0.006 cm2
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