Given the relative error in the measurement of the radius of a circle is 0.02, What
measurement of its area?
of a circle is 0.02, what is the percentage error in the
the measurement of its area
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The percentage error in the measurement of its area is 4%.
Let the radius of the circle be 'r'.
We know, for a circle of radius 'r' cm, its area (A) is:
A = Пr²
Given that the error in the radius of the circle is 0.02
∴ Error = (Δr/r) = 0.02
So, error in volume would be (ΔA/A) = (П × 2r × Δr)/(Пr²)
[ d(r²)/dr = 2r]
= 2 × Δr/r [Δr/r = 0.02]
= 2 × 0.02
= 0.04
= [0.04 × 100]% = 4%
= 4% error in area.
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