What is the area and its approximate uncertainty, of a circle of radius 3.4 x 10^4 cm?

Question

What is the area and its approximate uncertainty, of a circle of radius 3.4 x 10^4 cm?

Answer 1

The area is:

pi * r^2 =

pi * (3.4 * 10^4 cm)^2

Since pi is an infinite, non-repeating irrational, the approximate uncertainty is r^2 times the difference between the value that you use for pi and the value of pi carried out to the next digit.

e.g.; (3.14 - 3.142 = -0.002); (3.1416 - 3.14159 = +0.00001); etc.