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, we will use the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.

a. To find the value of A, we need to substitute the measured radius into the formula. Given that the radius is 10 cm with an uncertainty of dr = +/- 3 mm, we need to convert the uncertainty to centimeters for consistency. 3 mm is equal to 0.3 cm. Therefore, we have r = 10 cm +/- 0.3 cm.

Using the formula for the area of a circle, A = πr^2:
A = π(10 cm)^2 = 100π cm^2.

Thus, A = 100π cm^2. This is the value of A without considering the uncertainty.

b. To find the uncertainty in the area, we need to calculate the maximum and minimum values of the radius and then determine the corresponding maximum and minimum areas.

Maximum radius = 10 cm + 0.3 cm = 10.3 cm.
Minimum radius = 10 cm - 0.3 cm = 9.7 cm.

Using the formula for the area of a circle, A = πr^2:
Maximum area: A_max = π(10.3 cm)^2.
Minimum area: A_min = π(9.7 cm)^2.

Calculating these values:
A_max = π(10.3 cm)^2 = 105.639 cm^2.
A_min = π(9.7 cm)^2 = 93.238 cm^2.

Therefore, the uncertainty in the area, a, is equal to the difference between the maximum and minimum areas:
a = A_max - A_min = 105.639 cm^2 - 93.238 cm^2 = 12.401 cm^2.

So, the uncertainty in the area of the circular table is a = 12.401 cm^2.