Question

The error in the measurement of diameter of a
Circular disc is 2%. The percentage error in the
measurement of the area is ?​

Answer 1

As all of know surface area of the sphere is calculated by the formula 4πr*r . So it is clear area of the sphere is directly proportional to square of its radius.

Now there are two chance, either you over measured the radius or under measured.

Let x - surface area of the sphere when radius of sphere is y.

CASE 1:

If radius is over measured by 2%, that is instead of measuring it as y you measured it as y+2% of y = y+ 0.02y.

x= 4 π (y)^2

?= 4 π ( y+0.02y)^2

By solving this you'll get the new surface area as 1.0404x. Now error will be relative error. It will be 1.0404x-x/x = 0.0404 , in terms of % it is 4.04%

Case2:

If radius is under measured by 2 %,

x= 4 π (y)^2

?= 4 π ( y-2)^2

Then new surface area is 0.9604x. Error will be 0.0396 & in terms of % it is 3.96%

I HOPE it's HELPFUL for you