Question

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​

Answer 1

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.