Problem 2E

A measurement of the circumference of a disk has an uncertainty of 1.5 mm. How many measurements must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm?

Solution 2E

Step1 of 2:

We have A disk and let X be the measurement of the circumference of a disk has an uncertainty of 1.5 mm. Let Y be the measurement of the diameter of a disk has an uncertainty of 0.5 mm.

That is .

We need to find How many measurements must be made so that the diameter can be estimated with an uncertainty of only 0.5 mm.

Step2 of 2:

Consider

The circumference of disk is given by C =

Where

C = circumference

mathematical constant and its value is 3.14

r = radius

=

=

= 0.25

Now,

C =

= 2(3.14)(0.25)

= 1.5

1.5

3

= 9

Therefore, n = 9.