Question

The diameter of a circle found by measurement $5.2$cms with a maximum error $0.05$cms Then the maximum error in its area is?

• A. $4.1$ sq. cms
• B. $0.041$ sq. cms
• C. $0.41$ sq. cms
• D. $0.5$ sq. cms

Answer 1

Answer: (C)

$0.41$ sq. cms

The Actual diameter $=5.2-0.05=5.15cm$

So, Actual Radius $=\frac{5.15}{2}=2.575cm$

Actual Area of circle $=\pi r^2=\frac{2}{7}\times (2.575{)}^2=20.839c{m}^2$

The calculated area of circle $=\pi r^2=\frac{22}{7}(2.6{)}^2=21.245c{m}^2$

Thus, Maximum error in area $=21.245-20.839=0.41c{m}^2$

So, $\text{C}$ is correct option.