Suppose you have a circle with a radius of 6.43 ± 0.09 m, what is the average area of the circle?
A=pi*r^2 = 3.142 * (6.43)^2 = 129.89m^2
To find the average area of the circle, you'll need to use the formula for the area of a circle and consider the uncertainty in the radius.
The formula for the area of a circle is A = π * r^2, where A represents the area and r represents the radius.
In this case, the given radius is 6.43 ± 0.09 m. The ± 0.09 m indicates the uncertainty or the range of possible values for the radius.
To calculate the average area, you'll need to consider the lower and upper limits of the radius.
Lower limit: radius = 6.43 - 0.09 = 6.34 m
Upper limit: radius = 6.43 + 0.09 = 6.52 m
Let's calculate the average area now.
Average Area = (Area at lower limit + Area at upper limit) / 2
Area at lower limit = π * (radius at lower limit)^2
Area at lower limit = π * (6.34)^2
Area at upper limit = π * (radius at upper limit)^2
Area at upper limit = π * (6.52)^2
Now you have the areas at the lower and upper limits. You can calculate the average area by plugging these values into the formula:
Average Area = (π * (6.34)^2 + π * (6.52)^2) / 2
Calculating the average area will give you the desired result.
Keep in mind that π is a constant equal to approximately 3.14159, but you can also use more precise values if desired.