You have a circular table. You measured its radius to be 10 cm with an uncertainty dr =+/- 3mm. The area would be A +/- a cm^2.

a. What is A?
b. What is a?

To find the area of a circular table, you can use the formula A = πr², where A represents the area and r represents the radius.

a. What is A?
To find A, you simply substitute the given value of the radius into the formula. So, A = π(10 cm)².

To calculate A with the given uncertainty, we need to consider the maximum and minimum values of the radius. The maximum value will be 10 cm + 3 mm = 10.3 cm, and the minimum value will be 10 cm - 3 mm = 9.7 cm.

Using these values, we can calculate the maximum value of A by substituting the maximum value of the radius: A(max) = π(10.3 cm)².
Similarly, we can calculate the minimum value of A by substituting the minimum value of the radius: A(min) = π(9.7 cm)².

Therefore, the area of the circular table A will be within the range of A(min) to A(max).

b. What is a?
To find the uncertainty (a) in the area, we can use the following formula:

a = |A(max) - A(min)| / 2

By substituting the maximum and minimum values of A into the formula, we can calculate the uncertainty:

a = |π(10.3 cm)² - π(9.7 cm)²| / 2