The calculated area's maximum percentage relative error is approximately 1.33%.
we know that:
Area of the circular disc is given by A = πr²
consider A = πr²
Differentiate both sides with respect to r, we get
dA/dr = 2πr
⇒ dA = 2πr dr
calculate area:
A = πr²
A = π(30)²
A = 900π
A = 2826 cm²
Because of an error in measurement, the radius might actually be as big as 30+0.2 cm
= 30.2 cm
If r is increased from 30 by an amount Δr = dr = 0.2
Then the actual change in the calculated area would be :
ΔA = A(30+Δr)-A(30)
ΔA = A(30.2)-A(30)
ΔA = (30.2)²π - 900π
ΔA = 912.04π - 900π
= 12.04π cm²
So we estimated the maximum error in calculated area as 12.04π cm²
≅ 37.8 cm²
The maximum relative error in calculated area is:
ΔA/A= dA/A = 12.04π/900π
= 0.013
= 1.33 %
The maximum % relative error in calculated area is about 1.33%.
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