The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. What is the relative error? What is the percentage error?

Solution:

Radius of a circular disk = 24 cm

Area of a circular disk can be written as A = πr²

Now differentiate both sides with respect to r

dA/dr = 2πr

dA = 2πr dr

First calculate the area

A = π × (24)²

A = 576π cm²

A = 1809.6 cm²

Due to the error in measurement, the radius is big as 24 + 0.02

If the radius is increased from 24 by Δr = dr = 0.02

Actual change in the calculated area ΔA = A(24 + Δr) - A(24)

So we get,

= A(24.02) - A(24)

ΔA = dA = A(24.02) - A(24)

So we get,

= π × (24.02)² - 576π

= 576.96π - 576π

= 0.96π cm²

The maximum error in calculated area is ΔA/A ≈ dA/A = 0.96π/576π = 0.96/576 ≈ 0.0017

The maximum percentage relative error in the area calculated is 0.17%

Therefore, the relative error is 0.0017 and the percentage error is 0.17%.

---

The radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm. What is the relative error? What is the percentage error?

Summary:

If the radius of a circular disk is given as 24 cm with a maximum error in measurement of 0.2 cm then the relative error is 0.0017 and the percentage error is 0.17%.