Question

10. In measuring the circumference 100cm of a
circle, there is an error of 0.05 cm then the
percentage error in its area is
-
SE
10
3) 100
4)1
to​

Answer 1

Given:

Circumference of the circle , C = 100cm.

Error measured in circumference dc = 0.05 cm

To Find:

Percentage error in its area.

Solution:

Let A be the area of the circle.

dA be the error measured in its area.

Now we know,

• C = 2πr
• dc = 2πdr
• dr = dc/2π = 0.05/2π

Also, r = C/2π

Therefore error in radius = dr = 0.05/2π cm .

We know,

• Area , A = πr²
• dA = 2πrdr.
• Percentage error in area,
• dA/A = 2πrdr/πr² = 2dr/r

• dA/A = 2 x 0.05/2π x 2π/C = 0.1/100 .

Percentage error in area is :

• da/A x 100 = 0.1 %

The percentage error in its area is 0.1%